Interpolation in Jacobi-weighted spaces and its application to a posteriori error estimations of the p-version of the finite element method

Abstract

The goal of this work is to introduce a local and a global interpolator in Jacobi-weighted spaces, with optimal order of approximation in the context of the $p$-version of finite element methods. Then, an a posteriori error indicator of the residual type is proposed for a model problem in two dimensions and, in the mathematical framework of the Jacobi-weighted spaces, the equivalence between the estimator and the error is obtained on appropriate weighted norm.