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•   QUADRATURE BASED FINITE ELEMENT METHODS FOR LINEAR PARABOLIC INTERFACE PROBLEMS

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.

• Quadrature based finite element methods for linear parabolic interface problems

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. 