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

Albright, Jason; Epshteyn, Yekaterina; Xia, Qing

Commun. Math. Sci. 15, No. 4, 985-1019 (2017).

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

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