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Home  >  Transactions of NAMP VOL 6

25. Convergence of a finite element solution for a nonlinear parabolic equation with discontinuous coefficient by M. O. Adewolea and V. F. Payne Transactions Vol. 6 (Jan., 2018), pp. 213{ 227
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Convergence of a finite element solution for a nonlinear parabolic

equation with discontinuous coefficient

M. O. Adewolea and V. F. Payne

Department of Mathematics, University of Ibadan, Nigeria

Abstract. 

Solution of a nonlinear parabolic interface problem with Finite Element-Backward Di erence

Scheme (FE-BDS) is presented. The convergence of the scheme on a two-dimensional convex polygonal

domain is analyzed. Error estimates of optimal order in the L2(0; T;L2(

))-norm and L2(0; T;H1(

))-

norm are determined for spatially discrete scheme. A fully discrete scheme based on 2-step BDS is analyzed.

Numerical experiment is presented to support the theoretical result. It is assumed that the interface could

be fitted exactly.

Keywords: interface, semi-discrete, fully discrete, optimal error estimates

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