Functional A Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems

A functional type a posteriori error estimator for the finite element dis-cretization of the stationary reaction-convection-diffusion equation is derived. In caseof dominant convection, the solution for this class of problems typically exhibits bound-ary layers and shock-front like areas with steep gradients. This renders the accuratenumerical solution very demanding and appropriate techniques for the adaptive resolu-tion of regions with large approximation errors are crucial. Functional error estimatorsas derived here contain no mesh-dependent constants and provide guaranteed errorbounds for any conforming approximation. To evaluate the error estimator, a mini-mization problem is solved which does not require any Galerkin orthogonality or anyspecific properties of the employed approximation space. Based on a set of numericalexamples, we assess the performance of the new estimator. It is observed that it ex-hibits a good efficiency also with convection-dominated problem settings