INEXACT SOLVERS ON ELEMENT INTERFACES FOR THE P-FINITE-ELEMENT AND H-P-FINITE-ELEMENT METHOD

Parallel and iterative solvers for large-scale linear system arising f rom finite element discretization, based on domain decomposition, deco mpose the approximation spaces into a number of subspaces. The corresp onding subproblems are solved in these subspaces, and the solutions ar e corrected in an iterative process. The subproblems are much smaller in size and much easier to be solved. One of these subspaces is spanne d by (high order) element side modes in two dimensions and (high order ) element face modes in three dimensions. Solving the subproblems on t he element interfaces is a major cost in each step of iteration. To re duce computational cost, various inexact solvers on element interfaces are proposed in this paper, with theoretical analysis and numerical i llustrations.