Additive Schwarz Preconditioning for p-Version Triangular and Tetrahedral Finite Elements

This paper analyzes two-level Schwarz methods for matrices arising from the p-version finite element method on triangular and tetrahedral meshes. The coarse level consists of the lowest order finite element space. On the fine level, we investigate sev-eral decompositions with large or small overlap leading to optimal or close to optimal condition numbers. The analysis is confirmed by numerical experiments for a simple model problem and an elasticity problem on a complex geometry. High Order Finite Element Method, Preconditioning.