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

Johnson, Claes; Larsson, Stig; Thomée, Vidar; Wahlbin, Lars B.

doi:10.1090/S0025-5718-1987-0906175-1

Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data
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by Claes Johnson, Stig Larsson, Vidar Thomée and Lars B. Wahlbin PDF

Math. Comp. 49 (1987), 331-357 Request permission

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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