WIAS Preprint No. 1747, (2012)

Numerical convergence for semilinear parabolic equations



Authors

  • Huth, Robert

2010 Mathematics Subject Classification

  • 47N40 65J15

Keywords

  • numerical analysis, semilinear parabolic equation, sectorial operators

Abstract

We present a convergence result for finite element discretisations of semilinear parabolic equations, in which the evaluation of the nonlinearity requires some high order of regularity of the solution. For example a coefficient might depend on derivatives or pointevaluation of the solution. We do not rely on high regularity of the exact solution itself and as a payoff we can not deduce convergence rates. As an example the convergence result is applied to a nonlinear Fokker--Planck type battery model.

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