A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems. (30th July 2015)

• Record Type: Journal Article
• Authors: Chen, Xingding; Yuan, Guangwei
• Is Part Of: Communications in computational physics. Volume 18:Number 2(2015:Aug.)
• Page Start: 297
• Page End: 320
• Publication Date: 2015-07-30
• Subjects: Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.120914.311214a
• Languages: English
• ISSNs: 1815-2406

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>In this paper, we are concerned with the constrained finite element method based on domain decomposition satisfying the discrete maximum principle for diffusion problems with discontinuous coefficients on distorted meshes. The basic idea of domain decomposition methods is used to deal with the discontinuous coefficients. To get the information on the interface, we generalize the traditional Neumann-Neumann method to the discontinuous diffusion tensors case. Then, the constrained finite element method is used in each subdomain. Comparing with the method of using the constrained finite element method on the global domain, the numerical experiments show that not only the convergence order is improved, but also the nonlinear iteration time is reduced remarkably in our method.</p> </abstract>