Towards optimal finite element error estimates for the penalized Dirichlet problem in a domain with curved boundary

摘要

We consider the finite element approximation of an elliptic problem with homogeneous Dirichlet boundary conditions on a curved boundary and imposed using the penalty method. We establish optimal H-1 error estimates with suitable assumptions on the penalty parameter epsilon as a function of the elements size h. Our focus is on establishing these results with least restrictive assumptions possible on this dependency. (C) 2015 Elsevier Ltd. All rights reserved.