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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
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 $ {L^2}$) 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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Keywords: Finite elements, parabolic equations, backward Euler method
Article copyright: © Copyright 1993 American Mathematical Society