Some interior estimates for semidiscrete Galerkin approximations for parabolic equations
Author:
Vidar Thomée
Journal:
Math. Comp. 33 (1979), 3762
MSC:
Primary 65N30; Secondary 65M15
MathSciNet review:
514809
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Abstract: Consider a solution u of the parabolic equation where A is a second order elliptic differential operator. Let ; h small denote a family of finite element subspaces of which permits approximation of a smooth function to order . Let and assume that is an approximate solution which satisfies the semidiscrete interior equation where denotes the bilinear form on associated with A. It is shown that if the finite element spaces are based on uniform partitions in a specific sense in , then difference quotients of may be used to approximate derivatives of u in the interior of to order provided certain weak global error estimates for to this order are available. This generalizes results proved for elliptic problems by Nitsche and Schatz [9) and Bramble, Nitsche and Schatz [1].
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905148094
PII:
S 00255718(1979)05148094
Article copyright:
© Copyright 1979
American Mathematical Society
