Scott, L. Ridgway
Overview
Works:  43 works in 164 publications in 2 languages and 2,946 library holdings 

Genres:  Conference papers and proceedings Academic theses History 
Roles:  Author, Editor, htt 
Classifications:  QA379, 515.35 
Publication Timeline
.
Most widely held works by
L. Ridgway Scott
The mathematical theory of finite element methods by
Susanne C Brenner(
Book
)
62 editions published between 1994 and 2011 in English and Undetermined and held by 1,598 WorldCat member libraries worldwide
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'eFriedrichs inequalities for piecewise Ŵ1_p functions. New exercises have also been added throughout. The initial chapter provides an introducton to the entire subject, developed in the onedimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to:  multigrid methods and domain decomposition methods  mixed methods with applications to elasticity and fluid mechanics  iterated penalty and augmented Lagrangian methods  variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods  error estimates in the maximum norm with applications to nonlinear problems  error estimators, adaptive meshes and convergence analysis of an adaptive algorithm  Banachspace operatorinterpolation techniques The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency. Reviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a welldone text and a good reference." (Mathematical Reviews, 1995) "This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area." (Zentralblatt, 2002)
62 editions published between 1994 and 2011 in English and Undetermined and held by 1,598 WorldCat member libraries worldwide
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'eFriedrichs inequalities for piecewise Ŵ1_p functions. New exercises have also been added throughout. The initial chapter provides an introducton to the entire subject, developed in the onedimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to:  multigrid methods and domain decomposition methods  mixed methods with applications to elasticity and fluid mechanics  iterated penalty and augmented Lagrangian methods  variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods  error estimates in the maximum norm with applications to nonlinear problems  error estimators, adaptive meshes and convergence analysis of an adaptive algorithm  Banachspace operatorinterpolation techniques The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency. Reviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a welldone text and a good reference." (Mathematical Reviews, 1995) "This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area." (Zentralblatt, 2002)
Numerical analysis by
L. Ridgway Scott(
)
11 editions published in 2011 in English and held by 621 WorldCat member libraries worldwide
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and selfcontained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquirybased learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Selfcontained and mathematically rigorous Contains problems and solutions in each chapter Excellent followup course to Principles of Mathematical Analysis by Rudin
11 editions published in 2011 in English and held by 621 WorldCat member libraries worldwide
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and selfcontained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquirybased learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Selfcontained and mathematically rigorous Contains problems and solutions in each chapter Excellent followup course to Principles of Mathematical Analysis by Rudin
Scientific parallel computing by
L. Ridgway Scott(
Book
)
15 editions published between 2005 and 2006 in English and held by 397 WorldCat member libraries worldwide
From modelling financial markets to global weather patterns, parallel computing enables computations beyond the reach of sequential methods. This text integrates all the fundamentals of parallel computing while also providing a basis for a deeper understanding of the subject
15 editions published between 2005 and 2006 in English and held by 397 WorldCat member libraries worldwide
From modelling financial markets to global weather patterns, parallel computing enables computations beyond the reach of sequential methods. This text integrates all the fundamentals of parallel computing while also providing a basis for a deeper understanding of the subject
A mathematical approach to protein biophysics by
L. Ridgway Scott(
)
11 editions published in 2017 in English and held by 235 WorldCat member libraries worldwide
This book explores quantitative aspects of protein biophysics and attempts to delineate certain rules of molecular behavior that make atomic scale objects behave in a digital way. This book will help readers to understand how certain biological systems involving proteins function as digital information systems despite the fact that underlying processes are analog in nature. The indepth explanation of proteins from a quantitative point of view and the variety of level of exercises (including physical experiments) at the end of each chapter will appeal to graduate and senior undergraduate students in mathematics, computer science, mechanical engineering, and physics, wanting to learn about the biophysics of proteins. L. Ridgway Scott has been Professor of Computer Science and of Mathematics at the University of Chicago since 1998, and the Louis Block Professor since 2001. He obtained a B.S. degree (Magna Cum Laude) from Tulane University in 1969 and a PhD degree in Mathematics from the Massachusetts Institute of Technology in 1973. Professor Scott has published over 130 papers and three books, extending over biophysics, parallel computing and fundamental computing aspects of structural mechanics, fluid dynamics, nuclear engineering, and computational chemistry. Ariel Fernández (born Ariel Fernández Stigliano) is an ArgentinianAmerican physical chemist and mathematician. He obtained his Ph. D. degree in Chemical Physics from Yale University and held the Karl F. Hasselmann Endowed Chair Professorship in Bioengineering at Rice University. He is currently involved in research and entrepreneurial activities at various consultancy firms. Ariel Fernández authored three books on translational medicine and biophysics, and published 360 papers in professional journals. He holds two patents in the field of biotechnology.
11 editions published in 2017 in English and held by 235 WorldCat member libraries worldwide
This book explores quantitative aspects of protein biophysics and attempts to delineate certain rules of molecular behavior that make atomic scale objects behave in a digital way. This book will help readers to understand how certain biological systems involving proteins function as digital information systems despite the fact that underlying processes are analog in nature. The indepth explanation of proteins from a quantitative point of view and the variety of level of exercises (including physical experiments) at the end of each chapter will appeal to graduate and senior undergraduate students in mathematics, computer science, mechanical engineering, and physics, wanting to learn about the biophysics of proteins. L. Ridgway Scott has been Professor of Computer Science and of Mathematics at the University of Chicago since 1998, and the Louis Block Professor since 2001. He obtained a B.S. degree (Magna Cum Laude) from Tulane University in 1969 and a PhD degree in Mathematics from the Massachusetts Institute of Technology in 1973. Professor Scott has published over 130 papers and three books, extending over biophysics, parallel computing and fundamental computing aspects of structural mechanics, fluid dynamics, nuclear engineering, and computational chemistry. Ariel Fernández (born Ariel Fernández Stigliano) is an ArgentinianAmerican physical chemist and mathematician. He obtained his Ph. D. degree in Chemical Physics from Yale University and held the Karl F. Hasselmann Endowed Chair Professorship in Bioengineering at Rice University. He is currently involved in research and entrepreneurial activities at various consultancy firms. Ariel Fernández authored three books on translational medicine and biophysics, and published 360 papers in professional journals. He holds two patents in the field of biotechnology.
ICOSAHOM 95 : proceedings of the Third International Conference on Spectral and High Order Methods : Houston, Texas, 59 June,
1995 by International Conference on Spectral and High Order Methods(
Book
)
1 edition published in 1996 in English and held by 10 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 10 WorldCat member libraries worldwide
An evaluation of a model equation for water waves by
J. L Bona(
Book
)
3 editions published in 1981 in English and held by 10 WorldCat member libraries worldwide
3 editions published in 1981 in English and held by 10 WorldCat member libraries worldwide
The Mathematical Theory of Finite Element Methods by
Susanne C Brenner(
)
2 editions published in 2008 in English and held by 9 WorldCat member libraries worldwide
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'eFriedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout. The initial chapter provides an introducton to the entire subject, developed in the onedimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to:  multigrid methods and domain decomposition methods  mixed methods with applications to elasticity and fluid mechanics  iterated penalty and augmented Lagrangian methods  variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods  error estimates in the maximum norm with applications to nonlinear problems  error estimators, adaptive meshes and convergence analysis of an adaptive algorithm  Banachspace operatorinterpolation techniques The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency. Reviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a welldone text and a good reference." (Mathematical Reviews, 1995) "This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area." (Zentralblatt, 2002)
2 editions published in 2008 in English and held by 9 WorldCat member libraries worldwide
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'eFriedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout. The initial chapter provides an introducton to the entire subject, developed in the onedimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to:  multigrid methods and domain decomposition methods  mixed methods with applications to elasticity and fluid mechanics  iterated penalty and augmented Lagrangian methods  variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods  error estimates in the maximum norm with applications to nonlinear problems  error estimators, adaptive meshes and convergence analysis of an adaptive algorithm  Banachspace operatorinterpolation techniques The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency. Reviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a welldone text and a good reference." (Mathematical Reviews, 1995) "This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area." (Zentralblatt, 2002)
ERROR ESTIMATES FOR GAUSSIAN QUADRATURE AND WEIGHTEDL1 POLYNOMIAL APPROXIMATION by
Ronald A DeVore(
Book
)
5 editions published in 1981 in English and Undetermined and held by 5 WorldCat member libraries worldwide
Error estimates for Gaussian quadrature are given in terms of the number of quadrature points and smoothness properties of the function whose integral is being approximated. An intermediate step involves a weightedL polynomial approximation problem which is treated in a more general context than that specifically required to estimate the Gaussian quadrature error
5 editions published in 1981 in English and Undetermined and held by 5 WorldCat member libraries worldwide
Error estimates for Gaussian quadrature are given in terms of the number of quadrature points and smoothness properties of the function whose integral is being approximated. An intermediate step involves a weightedL polynomial approximation problem which is treated in a more general context than that specifically required to estimate the Gaussian quadrature error
Numerical schemes for a model for nonlinear dispersive waves by
Mathematics Research Center (United States. Army)(
Book
)
4 editions published in 1983 in English and Undetermined and held by 5 WorldCat member libraries worldwide
A description is given of a number of numerical schemes to solve an evolution equation (KortewegdeVries) that arises when modelling the propagation of water waves in a channel. The discussion also includes the results of numerical experiments made with each of the schemes. It is suggested, on the basis of these experiments, that one of the schemes may have (discrete) solitarywave solutions. (Author)
4 editions published in 1983 in English and Undetermined and held by 5 WorldCat member libraries worldwide
A description is given of a number of numerical schemes to solve an evolution equation (KortewegdeVries) that arises when modelling the propagation of water waves in a channel. The discussion also includes the results of numerical experiments made with each of the schemes. It is suggested, on the basis of these experiments, that one of the schemes may have (discrete) solitarywave solutions. (Author)
A comparison of solutions of two model equations for long waves by
J. L Bona(
Book
)
4 editions published in 1983 in English and Undetermined and held by 5 WorldCat member libraries worldwide
This paper is concerned with mathematical models representing the unidirectional propagation of weakly nonlinear dispersive waves. Interest will be directed toward two particular models that are originally studied in the context of surfacewave phenomena in openchannel flows. The purpose of the present paper is to make a quantitative comparison between the solutions to the initialvalue problem for each of these models. The basic conclusion of the study is that, on a long time scale T naturally related to the underlying physical situation, the equations predict the same outcome to within their implied order of accuracy. In this case the choice of one of these models over the other to describe a physical problem is apparently immaterial, with factors of incidental convenience probably providing the main criteria in a given situation. (Author)
4 editions published in 1983 in English and Undetermined and held by 5 WorldCat member libraries worldwide
This paper is concerned with mathematical models representing the unidirectional propagation of weakly nonlinear dispersive waves. Interest will be directed toward two particular models that are originally studied in the context of surfacewave phenomena in openchannel flows. The purpose of the present paper is to make a quantitative comparison between the solutions to the initialvalue problem for each of these models. The basic conclusion of the study is that, on a long time scale T naturally related to the underlying physical situation, the equations predict the same outcome to within their implied order of accuracy. In this case the choice of one of these models over the other to describe a physical problem is apparently immaterial, with factors of incidental convenience probably providing the main criteria in a given situation. (Author)
What Kind of Workstation Should I Buy? SevenFold Criteria for Hardware and Software by
L. Ridgway Scott(
Book
)
4 editions published in 1985 in English and Undetermined and held by 4 WorldCat member libraries worldwide
The problem of designing a workstation suitable for an individual scientist or group of scientists are addressed from an abstract point of view. A set of seven criteria concerning hardware are presented that should be considered when assessing one's needs and comparing various available products. Seven categories of software are also discussed that are critical for someone doing code development, testing and production runs on a remote computer (mainframe or supercomputer). The criteria discussed are intended to be a model checklist relevant especially for people doing code development and production work in scientific computation. After discussing criteria for evaluating workstations, two examples are given of inexpensive yet powerful systems that should be possible to assemble today. (Author)
4 editions published in 1985 in English and Undetermined and held by 4 WorldCat member libraries worldwide
The problem of designing a workstation suitable for an individual scientist or group of scientists are addressed from an abstract point of view. A set of seven criteria concerning hardware are presented that should be considered when assessing one's needs and comparing various available products. Seven categories of software are also discussed that are critical for someone doing code development, testing and production runs on a remote computer (mainframe or supercomputer). The criteria discussed are intended to be a model checklist relevant especially for people doing code development and production work in scientific computation. After discussing criteria for evaluating workstations, two examples are given of inexpensive yet powerful systems that should be possible to assemble today. (Author)
Introduction to Automated Modeling with FEniCS by
L. Ridgway Scott(
Book
)
2 editions published in 2018 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2018 in English and held by 3 WorldCat member libraries worldwide
Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon by
University of Minnesota(
Book
)
3 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide
Consider the existence of regular solutions to the boundary value problem div U = f on a plane polygonal domain Omega with the Dirichlet boundary condition U = g on del Omega. We formulate simultaneously necessary and sufficient conditions on f and g in order that a solution U exist in the Sobolev space W (over s+1 to p) (Omega). In addition to the obvious regularity and integral conditions these consist of at most one compatibility condition at each vertex of the polygon. In the special case of homogeneous boundary data, it is necessary and sufficient that f belong to W (over s to p) (Omega), have mean value zero, and vanish at each vertex. (The latter condition only applies if s is large enough that the point values make sense.) We construct a solution operator which is independent of s and p. Various new trace theorems for Sobolev spaces on polygons are obtained. Keywords: Divergence; Trace; Sobolev space; Reprints
3 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide
Consider the existence of regular solutions to the boundary value problem div U = f on a plane polygonal domain Omega with the Dirichlet boundary condition U = g on del Omega. We formulate simultaneously necessary and sufficient conditions on f and g in order that a solution U exist in the Sobolev space W (over s+1 to p) (Omega). In addition to the obvious regularity and integral conditions these consist of at most one compatibility condition at each vertex of the polygon. In the special case of homogeneous boundary data, it is necessary and sufficient that f belong to W (over s to p) (Omega), have mean value zero, and vanish at each vertex. (The latter condition only applies if s is large enough that the point values make sense.) We construct a solution operator which is independent of s and p. Various new trace theorems for Sobolev spaces on polygons are obtained. Keywords: Divergence; Trace; Sobolev space; Reprints
Bismarck  and a policy of "blood and iron" by
L. Ridgway Scott(
Book
)
2 editions published in 1972 in German and English and held by 3 WorldCat member libraries worldwide
2 editions published in 1972 in German and English and held by 3 WorldCat member libraries worldwide
Error estimates for the combined spatial and angular approximations of the transport equation for slab geometry by
J Pitkaeranta(
Book
)
2 editions published in 1982 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1982 in English and held by 3 WorldCat member libraries worldwide
Solving Galerkin approximations to nonlinear twopoint boundary value problems by a globally convergent homotopy method by
Layne T Watson(
Book
)
3 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
The mathematical theory of finite element models by
Susanne C Brenner(
Book
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
The Mathematical methods of finite element methods by
Susanne C Brenner(
Book
)
2 editions published between 1994 and 2002 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1994 and 2002 in English and held by 2 WorldCat member libraries worldwide
The Mathematical theory of finite elements methods by
Susanne C Brenner(
Book
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
Magistic militum of the eastern roman empire in the fifth century by
L. Ridgway Scott(
Book
)
2 editions published in 1972 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1972 in English and held by 2 WorldCat member libraries worldwide
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Algorithms Biomathematics BiophysicsMathematics Bismarck, Otto,Fürst von, Boundary value problems Boundary value problemsNumerical solutions Clinical biochemistry Computational intelligence Computer scienceMathematics ComputersResearch Differential equations, Partial Differential equations, PartialNumerical solutions Engineering Engineering mathematics Finite element method Finite element methodMathematics Functional analysis Gaussian quadrature formulas Germany Mathematical physics Mathematics Mechanics Mechanics, Applied Numerical analysis Parallel processing (Electronic computers) Polynomials Proteins Spectral theory (Mathematics) Systems biology VirginiaBlacksburg Wave equation WavesMathematical models