Finite difference schemes with transferable interfaces for parabolic problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:375

Article

Eriksson, Sofia¹  Nordstrom, Jan² 

[1] Linnaeus Univ, Fac Technol, Dept Math, S-35195 Vaxjo, Sweden

[2] Linkoping Univ, Dept Math, Computat Math, S-58183 Linkoping, Sweden

关键词: Finite difference methods;    Summation-by-parts;    High order accuracy;    Dual consistency;    Superconvergence;    Interfaces;   

DOI  :  10.1016/j.jcp.2018.08.051

来源: Elsevier

【 摘 要 】

We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free