Elliptic Problems in Curved Domains Using Cubature Points Based Triangular Spectral Elements and Isoparametric Mappings

Abstract

Using the cubature points based triangular spectral element method and isoparametric mappings, we provide accuracy results for elliptic problems in non polygonal domains. Two regimes of convergence, associated to the bulk and to the boundary of the computational domain are clearly discerned and an efficient way to define the isoparametric mapping is proposed.