Douglas, Jim Jr
Overview
Works:  37 works in 81 publications in 3 languages and 823 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Opponent, Other 
Classifications:  QA3, 510.8 S 
Publication Timeline
.
Most widely held works by
Jim Douglas
Collocation methods for parabolic equations in a single space variable, based on C¹ piecewisepolynomial spaces by
Jim Douglas(
Book
)
26 editions published between 1974 and 2008 in 3 languages and held by 458 WorldCat member libraries worldwide
26 editions published between 1974 and 2008 in 3 languages and held by 458 WorldCat member libraries worldwide
Flow in porous media : proceedings of the Oberwolfach Conference, June 2127, 1992 by Oberwolfach Conference(
Book
)
8 editions published in 1993 in English and held by 172 WorldCat member libraries worldwide
The papers deal with aspects of modeling, mathematical theory, numerical methods and applications in the engineering sciences
8 editions published in 1993 in English and held by 172 WorldCat member libraries worldwide
The papers deal with aspects of modeling, mathematical theory, numerical methods and applications in the engineering sciences
A quasiprojection approximation method applied to Galerkin procedures for parabolic and hyperbolic equations by
Jim Douglas(
Book
)
6 editions published in 1974 in English and Undetermined and held by 5 WorldCat member libraries worldwide
A technical method of approximating the Galerkin approximation to solutions of parabolic and hyperbolic equations can be based on a finite sequence of elliptic projections. The resulting function is called a quasiprojection, and it is used to study superconvergence phenomena associated with the Galerkin procedures
6 editions published in 1974 in English and Undetermined and held by 5 WorldCat member libraries worldwide
A technical method of approximating the Galerkin approximation to solutions of parabolic and hyperbolic equations can be based on a finite sequence of elliptic projections. The resulting function is called a quasiprojection, and it is used to study superconvergence phenomena associated with the Galerkin procedures
A Galerkin Procedure for Approximating the Flux on the Boundary for Elliptic and Parabolic Boundary Value Problems by
Jim Douglas(
Book
)
5 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
Elliptic and parabolic boundary value problems are first solved approximately on a rectangle and then simple auxiliary calculations are performed on the Galerkin solution to produce higher order correct approximations to the boundary flux than arise from the straightforward differentiation of the Galerkin solution. L sup 2 boundary and L sup infinity estimates are derived for the error. (Author)
5 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
Elliptic and parabolic boundary value problems are first solved approximately on a rectangle and then simple auxiliary calculations are performed on the Galerkin solution to produce higher order correct approximations to the boundary flux than arise from the straightforward differentiation of the Galerkin solution. L sup 2 boundary and L sup infinity estimates are derived for the error. (Author)
Collocation methods for parabolic equation in single space variable by
Jim Douglas(
Book
)
1 edition published in 1974 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1974 in English and held by 3 WorldCat member libraries worldwide
Approximate solution of physically unstable problems by Ecole d'Ete d'Analyse Numerique(
Book
)
1 edition published in 1965 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1965 in English and held by 3 WorldCat member libraries worldwide
Finite element method for differential equations. Cours enseigné a Orsay 1er semestre 197374 by
Jim Douglas(
Book
)
1 edition published in 1974 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1974 in English and held by 3 WorldCat member libraries worldwide
Flow in porous media : proceedings of the Oberwolfach conference on porous mediam(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Some superconvergence results for an H¹Galerkin procedure for the heat equation by
Jim Douglas(
Book
)
3 editions published in 1973 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1973 in English and held by 3 WorldCat member libraries worldwide
Modelling of compositional flow in naturally fractured reservoirs by
Zhangxin Chen(
)
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
Formulation of alternatingdirection iterative methods for mixed methods in three space by
Jim Douglas(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Attracteurs et variétés inertielles pour des équations dissipatives de la physique mathématique Champs markoviens et analyse
d'images by
Martine Marion(
Book
)
1 edition published in 1988 in French and held by 2 WorldCat member libraries worldwide
The works presented in this thesis concern the asymptotic behaviour (as t →∞ ) of dissipative partial differential equations and are mainly dealing with two topics: attractors and inertial manifolds.In the first part, we study the attractors associated with a rather general class of reaction diffusion systems (including systems with an invariant region). We consider both the dissipative case and the partly dissipative case more complex  where some diffusion coefficients are equal to zero. We prove the existence of universal attractors with finite fractal dimension and we derive estimates of this dimension. Our work relies in particular on generalizations of a class of collective functional inequalities due to Lieb and Thirring which are presented at the end of part one.The second part is devoted to inertial manifolds and their approximation. The existence of inertial manifolds for partly dissipative reactiondiffusion systems is established. We then address several questions related to approximate inertial manifolds. For reactiondiffusion equations, we show that such manifolds exist in high space dimension  as opposed to "exact" inertial manifolds. Then a method for constructing manifolds providing better and better order approximations to the solutions is presented in the case of the CahnHilliard equation. Lastly, we propose numerical schemes well adapted to the long term integration of partial differential equations and stemming from the study of approximate inertial manifolds.The third part deals with problems borrowed from the theory of combustion. We study the qualitative properties of a onedimensional stationary model for laminar flames. We also investigate the attractors associated with a twodimensional model in incompressible fluid
1 edition published in 1988 in French and held by 2 WorldCat member libraries worldwide
The works presented in this thesis concern the asymptotic behaviour (as t →∞ ) of dissipative partial differential equations and are mainly dealing with two topics: attractors and inertial manifolds.In the first part, we study the attractors associated with a rather general class of reaction diffusion systems (including systems with an invariant region). We consider both the dissipative case and the partly dissipative case more complex  where some diffusion coefficients are equal to zero. We prove the existence of universal attractors with finite fractal dimension and we derive estimates of this dimension. Our work relies in particular on generalizations of a class of collective functional inequalities due to Lieb and Thirring which are presented at the end of part one.The second part is devoted to inertial manifolds and their approximation. The existence of inertial manifolds for partly dissipative reactiondiffusion systems is established. We then address several questions related to approximate inertial manifolds. For reactiondiffusion equations, we show that such manifolds exist in high space dimension  as opposed to "exact" inertial manifolds. Then a method for constructing manifolds providing better and better order approximations to the solutions is presented in the case of the CahnHilliard equation. Lastly, we propose numerical schemes well adapted to the long term integration of partial differential equations and stemming from the study of approximate inertial manifolds.The third part deals with problems borrowed from the theory of combustion. We study the qualitative properties of a onedimensional stationary model for laminar flames. We also investigate the attractors associated with a twodimensional model in incompressible fluid
Recent results on mixed finite element methods for second order elliptic problems by
Italy) Istituto di analisi numerica (Pavia(
Book
)
1 edition published in 1984 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 2 WorldCat member libraries worldwide
Twophase immiscible flow in naturally fractured reservoirs by
University of Minnesota(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
Stabilized mixed methods for the Stokes problem by
University of Minnesota(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
Approximation of waves in composite media by
University of Minnesota(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
On the Numerical solution of a nonlinear firstorder differential equation by
Jim Douglas(
Book
)
1 edition published in 1959 in English and held by 1 WorldCat member library worldwide
1 edition published in 1959 in English and held by 1 WorldCat member library worldwide
Numerical simulation of immiscible flow in porous media based on combining the method of characteristics with mixed finite
element procedures by
University of Minnesota(
Book
)
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
1 edition published in 1987 in English and held by 1 WorldCat member library worldwide
An Approximate solution of an improper boundary value problem by
Jim Douglas(
Book
)
1 edition published in 1958 in English and held by 1 WorldCat member library worldwide
1 edition published in 1958 in English and held by 1 WorldCat member library worldwide
Some Superconvergence Results for an (H sup 1)Galerkin Procedure for the Heat Equation(
Book
)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
SDouglas, Jim, Jr.;Dupont, Todd ;Wheeler, Mary Fanett ;MRCTSR1382DA31124ARO(D)462Sponsored in part by National Science Foundation.*Heat transfer, *Partial differential equations, Calculus of variations, Convergence, Approximation, Theorems*Galerkin method, Parabolic differential equations, Heat equationThomee and Wahlbin have introduced a Galerkin method for the heat equation in a single space variable based on the (H sup 1)inner product and have obtained (H sup 2) and (H sup 1) estimates for the error. An (L sup 2) estimate is given here. The main object is to show knot superconvergence phenomena when the subspace is a piecewisepolynomial space. For (C sup 2)piecewisepolynomials of degree r, the error in the knot values is O(h sup(2r2)); for the (C sup 1) case, both knot values and knot first xderivatives are approximated to within O(h sup(2r2)). (Author)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
SDouglas, Jim, Jr.;Dupont, Todd ;Wheeler, Mary Fanett ;MRCTSR1382DA31124ARO(D)462Sponsored in part by National Science Foundation.*Heat transfer, *Partial differential equations, Calculus of variations, Convergence, Approximation, Theorems*Galerkin method, Parabolic differential equations, Heat equationThomee and Wahlbin have introduced a Galerkin method for the heat equation in a single space variable based on the (H sup 1)inner product and have obtained (H sup 2) and (H sup 1) estimates for the error. An (L sup 2) estimate is given here. The main object is to show knot superconvergence phenomena when the subspace is a piecewisepolynomial space. For (C sup 2)piecewisepolynomials of degree r, the error in the knot values is O(h sup(2r2)); for the (C sup 1) case, both knot values and knot first xderivatives are approximated to within O(h sup(2r2)). (Author)
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Related Identities
 Hornung, Ulrich 1941 Other Editor
 Dupont, Todd
 Conference on Porous Media 1992 Oberwolfach
 Wheeler, Mary F. (Mary Fanett)
 University of Minnesota Institute for Mathematics and Its Applications
 Duke University
 Todd, Dupont
 WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
 Brezzi, F.
 Chen, Zhangxin Author
Associated Subjects
Approximation theory Boundary value problems Collocation methods Convergence Differential equations Differential equations, HyperbolicNumerical solutions Differential equations, ParabolicNumerical solutions Fluid dynamics Galerkin methods Heat equation Mathematics Porous materials Projection Transport theory