ADDITIVE SCHWARZ METHOD FOR MORTAR DISCRETIZATION OF ELLIPTIC PROBLEMS WITH P_1 NONCONFORMING FINITE ELEMENTS

摘要

An additive Schwarz preconditioner for nonconforming mortar finite element discretization of a second order elliptic problem in two dimensions with arbitrary large jumps of the discontinuous coefficients in subdomains is described. An almost optimal estimate of the condition number of the preconditioned problem is proved. The number of preconditioned conjugate gradient iterations is independent of jumps of the coefficients and is proportional to (1 + log(H/h)), where H, h are mesh sizes.