An $hp$ finite element adaptive scheme on curved domains

MARIO SCHEBLE, MARÍA GABRIELA ARMENTANO, CLAUDIO PADRA

Buenos Aires

Congreso; MACI 2013 - IV Congreso de Matemática Aplicada, Computacional e Industrial; 2013

In this work we introduce and analyze an hp finite element method to solve a two-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 residual type, 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.