Communications in Mathematical Sciences
Volume 15 (2017)
High-order accurate methods based on difference potentials for 2D parabolic interface models
Pages: 985 – 1019
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.
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