Wavelet solvers for hp-FEM discretizations in 3D using hexahedral elements

In this paper we investigate the discretization of an elliptic boundary value problem in 3D by means of the hp  -version of the finite element method using a mesh of hexahedrons. The corresponding linear system is solved by a preconditioned conjugate gradient method. The construction of the preconditioner is based on an inexact additive overlapping Schwarz method. The remaining subproblems are treated by a tensor product based preconditioner. This preconditioner uses a basis transformation into a basis which is stable in L2L2 and H1H1. Several numerical examples show the efficiency of the proposed method.