Abstract
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.
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© 2006 Springer
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Thomée, V. (2006). Nonsmooth Data Error Estimates. In: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33122-0_3
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DOI: https://doi.org/10.1007/3-540-33122-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33121-6
Online ISBN: 978-3-540-33122-3
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