Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements

Jens M. Melenk ^{This paper analyses two-level Schwarz methods for matrices arisingfrom the p-version finite-element method on triangular and tetrahedralmeshes. The coarse level consists of the lowest-order finite-elementspace. On the fine level, we investigate several decompositionswith large or small overlap leading to optimal or close to optimalcondition numbers. The analysis is confirmed by numerical experimentsfor a simple model problem and an elasticity problem on a complexgeometry.}