FINITE ELEMENT METHOD FOR SECOND ORDER NONLINEAR PARABOLIC INTERFACE PROBLEMS

Abstract

Parabolic interface problems are frequently encountered as models of real-life situations and in scientific computing. This paper presents the error analysis of a second-order nonlinear parabolic interface problem with the Finite Element Method-Backward Difference Scheme (FEM-BDS). Quasiuniform triangular elements are used for the spatial discretization and a three-step linearized scheme is proposed for the time discretization. The stability of the scheme is established and an the almost optimal convergence rate is obtained. We also establish that the discrete solution reproduces the maximum principle under certain conditions. Numerical experiments are presented to support the theoretical results. It is assumed that the solution is of low regularity across the interface and the interface cannot be fitted exactly.