A modified bubble placement method and its application in solving elliptic problem with discontinuous coefficients adaptively. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Zhou, Yuqing; Nie, Yufeng; Zhang, Weiwei
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 6(2017)
• Page Start: 1268
• Page End: 1289
• Publication Date: 2017-06-03
• Subjects: Adaptive finite element method -- elliptic problem -- discontinuous coefficient -- force function -- constrained local mesh generation; 35R05 -- 65N50 -- 65M50 -- 74H15; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2016.1184258
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: To solve the elliptic problem with discontinuous coefficients adaptively and efficiently which has strong singularity, one of the key steps is to generate mesh adaptively near region with discontinuous coefficients according to an a posteriori error estimator. For bubble placement method, the previous interaction force function used to obtain a high-quality nodes set is only determined by the ratio ω of the real and desired distance between bubbles, which is not suitable to generate mesh with a very small size. In this study, the force function is modified and it is determined both by the ratio ω and the sizes of bubbles. Meanwhile, in consideration of the quality of nodes and the computational efficiency, the equation of motion used to calculate the positions of bubbles is also modified. Moreover, a constrained bubble-type local mesh generation (BLMG) method is developed. The modified node placement method and constrained BLMG strategy are applied to solve elliptic problem with discontinuous coefficients adaptively. Several numerical experiments are reported to demonstrate that the adaptive method can be applied to various kinds of complicated geometries, and the triangles remain very well shaped at any particular refinement levels, even though the mesh size varies by several orders of magnitude.