Analysis of a dual-primal FETI algorithm for edge elements on boundary layer meshes in two dimensions

Abstract

FETI methods are among the most heavily tested domain decomposition methods. The purpose of this thesis is to analyze a dual-primal FETI method for edge element approximations in two dimensions on geometrically refined meshes. These meshes are highly anisotropic, where the aspect ratio grows exponentially with the polynomial degree. The primal constraints are here averages over subdomain edges. We prove that the condition number of our algorithm grows only polylogarithmically with the polynomial degree and is independent of the aspect ratio of the mesh and of potentially large jumps of the coefficients.