Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2014; 51(3): 717-737

Printed May 31, 2014

https://doi.org/10.4134/BKMS.2014.51.3.717

Copyright © The Korean Mathematical Society.

Quadrature based finite element methods for linear parabolic interface problems

Bhupen Deka and Ram Charan Deka

Indian Institute of Technology Guwahati, Tezpur University

Abstract

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

Keywords: parabolic equation, interface, finite element method, optimal error estimates, quadrature

MSC numbers: 65N15, 65N30, 35R05