A Posteriori Error Estimates Based on Hierarchical Bases

Abstract

The authors present an analysis of an a posteriors error estimator based on the use of hierarchical basis functions. The authors analyze nonlinear, nonselfadjoint, and indefinite problems as well as the selfadjoint, positive-definite case. Because both the analysis and the estimator itself are quite simple, it is easy to see how various approximations affect the quality of the estimator. As examples, the authors apply the theory to some scalar elliptic equations and the Stokes system of equations.