A Numerical Method for Solving Elliptic Interface Problems Using Petrov-Galerkin Formulation with Adaptive Refinement. (10th September 2018)

• Record Type: Journal Article
• Authors: Wang, Liqun; Hou, Songming; Shi, Liwei
• Other Names: Salerno Nunzio Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2018(2018)
• Publication Date: 2018-09-10
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2018/3721258
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Elliptic interface problems have wide applications in engineering and science. Non-body-fitted grid has the advantage of saving the cost of mesh generation. In this paper, we propose a Petrov-Galerkin formulation using non-body-fitted grid for solving elliptic interface problems. In this method, adaptive mesh refinement is employed for cells with large errors. The new mesh still has all triangles being right triangles of the same shape. Numerical experiments show side-by-side comparison that to obtain the same accuracy, our new method has much less overall CPU time compared with the previous method even with some cost on mesh generation.