Exponential convergence in H1 of hp-FEM for Gevrey regularity with isotropic singularities

Abstract

For functions u∈ H1(Ω) in a bounded polytope Ω ⊂ Rdd= 1 , 2 , 3 with plane sides for d= 2 , 3 which are Gevrey regular in Ω ¯ \ S with point singularities concentrated at a set S⊂ Ω ¯ consisting of a finite number of points in Ω ¯ , we prove exponential rates of convergence of hp-version continuous Galerkin finite element methods on affine families of regular, simplicial meshes in Ω. The simplicial meshes are geometrically refined towards S but are otherwise unstructured.