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Nonsmooth Data Error Estimates

  • Vidar Thomée
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 25)

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.

Keywords

Positive Semidefinite Solution Operator Finite Element Solution Positive Time Galerkin Finite Element Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vidar Thomée
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden

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