Inexact additive Schwarz solvers for <em>hp</em>-FEM discretizations in three dimensions

Abstract

In this paper, a boundary value problem of second order in three space dimensions is discretized by means of the <em>hp</em>-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned conjugate gradient method with an overlapping domain decomposition preconditioner with inexact subproblem solvers. In addition to a global solver for the low order functions, the ingredients of this preconditioner are local solvers for the patches. Here, a solver is used which utilizes the tensor product structure of the patches. The efficiency in time and iteration numbers of the presented solver is shown in several numerical examples for diffusion like problems as well as for problems in linear elasticity.