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Quadrature based finite element methods for linear parabolic interface problems

Bhupen Deka|Ram Charan Deka
대한수학회 (The Korean Mathematical Society)|2014.05|대한수학회보 (Bulletin of the KMS)|제51권 제3호|pp. 717-737

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키워드

interfacefinite element methodquadratureparabolic equationoptimal error estimates
주제분류수학

초록

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal L2(L2) and L2(H1) error esti- mates are shown to hold for semidiscrete problem under suitable regular- ity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal L2(L2) norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

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 L2(L2) and L2(H1) error esti- mates are shown to hold for semidiscrete problem under suitable regular- ity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal L2(L2) norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

참고문헌 (24)

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