Kopteva, N,Linss, T,Dimov I,Farago I,Vulkov, L

NUMERICAL ANALYSIS AND ITS APPLICATIONS, NAA 2012

Numerical Study of Maximum Norm a Posteriori Error Estimates for Singularly Perturbed Parabolic Problems

2013

January

Published

1

()

a posteriori error estimate maximum norm singular perturbation elliptic reconstruction backward Euler Crank-Nicolson parabolic equation reaction-diffusion REACTION-DIFFUSION PROBLEM

50

61

A second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for two semidiscretisations in time and a full discretisation using P-1 FEM in space. Both the Backward-Euler method and the Crank-Nicolson method are considered. Certain critical details of the implementation are addressed. Based on numerical results we discuss various aspects of the error estimators in particular their effectiveness.