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Mathematics of Computation

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Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data

Authors: Claes Johnson, Stig Larsson, Vidar Thomée and Lars B. Wahlbin
Journal: Math. Comp. 49 (1987), 331-357
MSC: Primary 65N10; Secondary 65N30
MathSciNet review: 906175
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Abstract: We consider time-continuous spatially discrete approximations by the Galerkin finite element method of initial-boundary value problems for semilinear parabolic equations with nonsmooth or incompatible initial data. We find that the numerical solution enjoys a gain in accuracy at positive time of essentially two orders relative to the initial regularity, as a result of the smoothing property of the parabolic evolution operator. For higher-order elements the restriction to two orders is in contrast to known optimal order results in the linear case.

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Article copyright: © Copyright 1987 American Mathematical Society