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Published in:
2006 | OriginalPaper | Chapter
Nonsmooth Data Error Estimates
Author : Vidar Thomée
Published in: Galerkin Finite Element Methods for Parabolic Problems
Publisher: Springer Berlin Heidelberg
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In this chapter we shall first discuss a smoothing property of the solution operator of a homogeneous parabolic equation which shows that the solution is regular for positive time even if the initial data are not. We shall then demonstrate that an analogous behavior for the finite element solution implies that optimal order convergence takes place for positive time even for nonsmooth initial data. We also show some other results which elucidate the relation between the convergence of the finite element solution and the regularity of the exact solution.