A PRECONDITIONER FOR THE H-P VERSION OF THE FINITE-ELEMENT METHOD IN 2 DIMENSIONS

A preconditioner, based on a two-level mesh and a two-level orthogonal ization, is proposed for the h-p version of the finite element method for two dimensional elliptic problems in polygonal domains. Its implem entation is in parallel on the subdomain level for the linear or bilin ear (nodal) modes, and in parallel on the element level for the high o rder (side and internal) modes. The condition number of the preconditi oned linear system is of order [GRAPHICS] where H-i is the diameter of the i-th subdomain, h(i) and p(i) are the diameter of elements and th e maximum polynomial degree used in the subdomain. This result reduces to well-known results for the h-version (i.e. p(i) = 1) and the p-ver sion (i.e. h(i) = H-i) as the special cases of the h-p version.