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Some Superconvergence Results for an (H sup 1)-Galerkin Procedure for the Heat Equation.

Author: Jim Jr Douglas; Todd Dupont; Mary Fanett Wheeler; WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER.
Publisher: Ft. Belvoir Defense Technical Information Center DEC 1973.
Edition/Format:   Book : English
Database:WorldCat
Summary:
SDouglas, Jim, Jr.;Dupont, Todd ;Wheeler, Mary Fanett ;MRC-TSR-1382DA-31-124-ARO(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  Read more...
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Document Type: Book
All Authors / Contributors: Jim Jr Douglas; Todd Dupont; Mary Fanett Wheeler; WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER.
OCLC Number: 227569074
Notes: Sponsored in part by National Science Foundation.
Description: 26 p.

Abstract:

SDouglas, Jim, Jr.;Dupont, Todd ;Wheeler, Mary Fanett ;MRC-TSR-1382DA-31-124-ARO(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 piecewise-polynomial space. For (C sup 2)-piecewise-polynomials of degree r, the error in the knot values is O(h sup(2r-2)); for the (C sup 1) case, both knot values and knot first x-derivatives are approximated to within O(h sup(2r-2)). (Author).

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