Communications in Mathematical Sciences

Volume 15 (2017)

Number 4

High-order accurate methods based on difference potentials for 2D parabolic interface models

Pages: 985 – 1019

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n4.a4

Authors

Jason Albright (Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A.)

Yekaterina Epshteyn (Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A.)

Qing Xia (Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A.)

Abstract

Highly-accurate numerical methods that can efficiently handle problems with interfaces and/or problems in domains with complex geometry are essential for the resolution of a wide range of temporal and spatial scales in many partial differential equations based models from Biology, Materials Science and Physics. In this paper we continue our work started in 1D, and we develop high-order accurate methods based on the Difference Potentials for 2D parabolic interface/composite domain problems. Extensive numerical experiments are provided to illustrate high-order accuracy and efficiency of the developed schemes.

Keywords

parabolic problems, interface models, discontinuous solutions, difference potentials, finite differences, high-order accuracy in the solution and in the gradient of the solution, non-matching grids, parallel algorithms

2010 Mathematics Subject Classification

35K20, 65M06, 65M12, 65M22, 65M55, 65M70

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