Exponential convergence in H$^{1}$ of hp-FEM for Gevrey regularity with isotropic singularities

For functions u∈H$^{1}$(Ω) in a bounded polytope Ω⊂R$^{d}$, d=1,2,3 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 families of regular, simplicial meshes in Ω. The simplicial meshes are geometrically refined towards S but are otherwise unstructured.