An hp finite element adaptive scheme to solve the Poisson problem on curved domains

MARÍA G ARMENTANO, CLAUDIO PADRA, MARIO SCHEBLE

COMPUTATIONAL AND APPLIED MATHEMATICS

Springer

Año: 2015 vol. 34 p. 705 - 727

In this work we introduce an hp finite element method for two-dimensional Poisson problems on curved domains using curved elements. We obtain a priori  error estimates and define a local a posteriori error estimator of residual type.We show,  under appropriate assumptions about the curved domain, the globalreliability and the local efficiency of the esimator. More precisely, we prove that theestimator is equivalent to the energy norm of the error up to higher order terms. The equivalence constant of the efficiency estimate depends on the polynomial degree.We also present an hp adaptive algorithm and several numerical tests which show the performance of the adaptive strategy.