Analysis of a robust finite element approximation for a parabolic equation with rough boundary data

Authors:
Donald A. French and J. Thomas King

Journal:
Math. Comp. **60** (1993), 79-104

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1993-1153163-1

MathSciNet review:
1153163

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Abstract: The approximation of parabolic equations with nonhomogeneous Dirichlet boundary data by a numerical method that consists of finite elements for the space discretization and the backward Euler time discretization is studied. The boundary values are assumed in a least squares sense. It is shown that this method achieves an optimal rate of convergence for rough (only ) boundary data and for smooth data as well. The results of numerical computations which confirm the robust theoretical error estimates are also presented.

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1153163-1

Keywords:
Finite elements,
parabolic equations,
backward Euler method

Article copyright:
© Copyright 1993
American Mathematical Society