We address the solution of multiregion elliptic and parabolic problems with strongly discontinuous coefficients across interfaces. The underlying idea is, roughly, to perturb around the infinitely discontinuous coefficient solution, that is, to perturb the solution where one region is a perfect conductor. The result is partial decoupling of the interface conditions. The algorithm requires a sma...

Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a diffusion process with discontinuous diffusion and drift coefficients.

Abstract. Non-divergence form elliptic equations with discontinuous coefficients do not generally posses a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new hp-version discontinuous Galerkin finite element method for a class of these problems that satisfy the Cordès condition. It is shown that the method exhibits a co...