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. In this paper, we present the error analysis of a second order nonlinear parabolic interface problem with Finite Element Method-Backward Difference Scheme (FEM-BDS). Quasiuniformtriangular 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 almost optimal convergence rate is obtained. We also establish that the discrete solution reproduce 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.
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