Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem

Authors:
Ilia A. Brayanov;Juri D. Kandilarov;Miglena N. Koleva
Affiliations:
Department of Mathematics, University of Rousse, Rousse, Bulgaria 7017;Department of Mathematics, University of Rousse, Rousse, Bulgaria 7017;Department of Mathematics, University of Rousse, Rousse, Bulgaria 7017
Venue:
Large-Scale Scientific Computing
Year:
2009

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Abstract

Second order immersed interface difference schemes for a parabolic-elliptic interface problem arising in electromagnetism is presented. The numerical method uses uniform Cartesian meshes. The standard schemes are modified near the interface curve taking into account the specific jump conditions for the solution and the flux. Convergence of the method is discussed and numerical experiments, confirming second order of accuracy are shown.