An hp finite element adaptive scheme on curved domains

Abstract

In this work we introduce and analyze an hp finite element method to solve atwo-dimensional Poisson problem on curved domains by using curved elements.We obtain a priori error estimates and we develop an a posteriori error indicator of the residualtype, which results equivalent to the energy norm of the error up to higher order terms. We also present an hp adaptive algorithm and several numerical tests which allow us to show the optimal performance of the error indicator and the adaptive strategy.