WIAS Preprint No. 1936, (2014)

Functional a posteriori error estimation for stationary reaction-convection-diffusion problems



Authors

  • Eigel, Martin
  • Samrowski, Tatiana

2010 Mathematics Subject Classification

  • 65N30 65N15 65J15 65N22 65J10

Abstract

A functional type a posteriori error estimator for the finite element discretisation of the stationary reaction-convection-diffusion equation is derived. In case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shock-front like areas with steep gradients. This renders the accurate numerical solution very demanding and appropriate techniques for the adaptive resolution of regions with large approximation errors are crucial. Functional error estimators as derived here contain no mesh-dependent constants and provide guaranteed error bounds for any conforming approximation. To evaluate the error estimator, a minimisation problem is solved which does not require any Galerkin orthogonality or any specific properties of the employed approximation space. Based on a set of numerical examples, we assess the performance of the new estimator and compare it with some classic a posteriori error estimators often used in practice. It is observed that the new estimator exhibits a good efficiency also with convection-dominated problem settings.

Appeared in

  • Comput. Methods Appl. Math., 14 (2014) pp. 135--150.

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