Kopteva N.;Linß T.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Numerical study of maximum norm a posteriori error estimates for singularly perturbed parabolic problems

2013

November

Published

1

()

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

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 P1FEM 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. © 2013 Springer-Verlag.

10.1007/978-3-642-41515-9_5