AN ADDITIVE SCHWARZ METHOD FOR THE H-P VERSION OF THE FINITE-ELEMENT METHOD IN 3 DIMENSIONS

In this paper, we study the additive Schwarz method for the h-p versio n of the finite element method in three dimensions. The main idea is t o treat separately the h-version (linear) components and the p-version (high-order) components by a vertex-based method. It can also be view ed as a three-level method with the level being the linear finite elem ent approximation on the coarse mesh, the linear finite element approx imation on the fine mesh, and the high-order finite element approximat ion on the fine mesh, respectively. The resulting algorithm can be imp lemented in parallel on the subdomain level for the h-version componen ts and on the element level for the p-version components. The conditio n number is of order [GRAPHICS] where H-i stands for the diameter of t he subdomain Omega(i), h(i) is the diameter of the elements in Omega(i ), and p(i) is the maximum of the polynomial degrees used in Omega(i).