Additive Schwarz Methods for DG Discretization of Elliptic Problems with Discontinuous Coefficient

摘要

A nonoverlapping ASM for symmetric interior penalty DG discretization of second order elliptic PDE with discontinuous coefficient has been presented, in which a very large number of very small local problems is solved in parallel, together with one coarse problem of moderate size. Under mild assumptions, the condition number of the resulting system is O((H/h)~2), independently of the jumps of the coefficient.