Quadrature based finite element methods for linear parabolic interface problems
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 717-737
Published online May 31, 2014
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
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