Exponential convergence of simplicial hp-FEM for H^1-functions with isotropic singularities

For functions u ∈ H 1(Ω) in an open, bounded polyhedron Ω⊂Rd of dimension d = 1, 2, 3, which are analytic in Ω¯¯¯¯∖S with point singularities concentrated at the set S⊂Ω¯¯¯¯ consisting of a finite number of points in Ω¯¯¯¯, the exponential rate exp(−bN−−√d+1) of convergence of h p-version continuous Galerkin finite element methods on families of regular, simplicial meshes in Ω can be achieved. The simplicial meshes are assumed to be geometrically refined towards S and to be shape regular, but are otherwise unstructured.ISSN:1439-735