A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem

Abstract

Abstract.A coupling interface method (CIM) on uniform cartesian grid for solving parabolic-elliptic problems is proposed. The domain Ω is divided in two subregions Ω − and Ω + . On Ω − we consider an elliptic equation with nonlinear term and on Ω + -a linear parabolic equation. On the interface Γ the standard transmission conditions are stated: the jumps of the solution and the flux are zero. A method of upper and lower solutions is used to deal with the nonlinearity. Numerical experiments are discussed.