# 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.

## References

R. A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975.

M. O. Adewole, Almost optimal convergence of FEM-FDM for a linear parabolic interface problem, Electron. Trans. Numer. Anal. 46 337–358, 2017.

M. O. Adewole, H1-Convergence of FEM-BDS for Linear Parabolic Interface Problems, Journal of Computer Science & Computational Mathematics 8:3 49–54, 2018.

M. O. Adewole and V. F. Payne, Convergence of a Finite Element Solution for a Nonlinear Parabolic Equation with Discontinuous Coefficient, Transactions of the Nigerian Association of Mathematical Physics 6 213–227, 2018.

M. O. Adewole and V.F. Payne, Linearized four-step implicit scheme for nonlinear parabolic interface problems, Turkish J. Math. 42:6 3034–3049, 2018.

K. Atkinson and W. Han, Theoretical numerical analysis; A functional analysis framework, Texts in Applied Mathematics 39 Third Edition, Springer, Dordrecht, 2009.

S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, Texts in Applied Mathematics, 15, Third Edition, Springer, New York, 2008.

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## How to Cite

*Journal of the Nigerian Mathematical Society*,

*39*(1), 135-153. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/550