AN ADDITIVE SCHWARZ METHOD FOR THE h-p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS.

In this paper, we study the additive Schwarz method for the h-p version of the finite element method in three dimensions. The main idea is to treat separately the h-version (linear) components and the p-version (high-order) components by a vertex-based method. It can also be viewed as a three-level method with the level being the linear finite element approximation on the coarse mesh, the linear finite element approximation on the fine mesh, and the high-order finite element approximation on the fine mesh, respectively. The resulting algorithm can be implemented in parallel on the subdomain level for the h-version components and on the element level for the p-version components. The condition number is of order [This symbol cannot be presented in ASCII format](1 + ln H_ip_i/h_i)⇔2, where H_i stands for the diameter of the subdomain Ω_i, h_i is the diameter of the elements in Ω_i, and p_i is the maximum of the polynomial degrees used in Ω_i. [ABSTRACT FROM AUTHOR]