Numerical convergence for semilinear parabolic equations
- Huth, Robert
2010 Mathematics Subject Classification
- 47N40 65J15
- numerical analysis, semilinear parabolic equation, sectorial operators
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.