A-POSTERIORI FINITE-ELEMENT ERROR ESTIMATORS FOR INDEFINITE ELLIPTIC BOUNDARY-VALUE-PROBLEMS

Abstract

A general construction technique is presented for a posteriori error estimators of finite element solutions of elliptic boundary value problems that satisfy a Garding inequality. The estimators are obtained by an element-by-element solution of 'weak residual' problems with or without considering element boundary residuals. There is no order restriction on the finite element spaces used for the approximate solution or the error estimation; that is, the design of the estimators is applicable in connection with either one of the h-, p-, or hp- formulations of the finite element method. Under suitable assumptions it is shown that the estimators are bounded by constant multiples of the true error in a suitable norm. Some numerical results are given to demonstrate the effectiveness and efficiency of the approach.