×

zbMATH — the first resource for mathematics

High-order accurate methods based on difference potentials for 2D parabolic interface models. (English) Zbl 06751890
Summary: 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.

MSC:
35K20 Initial-boundary value problems for second-order parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI