Accurate Numeric Methods for Interface Problems with Strongly Discontinuous Coefficients

Daoqi Yang
Department of Mathematics, Wayne State University, Detroit, MI 48202, USA.

Standard finite difference, finite element, finite volume, or spectral methods are designed for problems with small and moderate coefficient discontinuities. Their accuracy deteriorates very rapidly when coefficient jumps are increased and can be arbitrarily bad for very large jumps. In this paper, an iterative numeric method is proposed and studied for solving interface problems modeled by second order partial differential equations with strongly discontinuous coefficients. The accuracy of this method does not deteriorate as the jump in the coefficient discontinuity goes to infinity. Numeric experiments in the object-oriented paradigm using C++ will be presented.