An efficient characteristic finite difference S-DDM scheme for convection–diffusion equations. (15th December 2020)

• Record Type: Journal Article
• Authors: Zhou, Zhongguo; Sun, Xinxin; Pan, Hao; Wang, Yan
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 12(2020)
• Page Start: 3044
• Page End: 3065
• Publication Date: 2020-12-15
• Subjects: Convection–diffusion equations -- S-DDM -- Characteristic difference -- Multi-block -- Convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.10.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, an efficient splitting domain decomposition method scheme for solving time-dependent convection–diffusion reaction equations is analyzed. A three-step method along each direction is used to solve the solution over each block-divided sub-domain at every time interval. The new solutions are firstly solved by the quadratic interpolation. Then, the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the new solutions. Lastly, the solutions and fluxes in the interiors of sub-domains are computed by the splitting implicit characteristic difference method. By some auxiliary lemmas and the defined intermediate exact solution, the stability and error estimate are given in discrete L 2 -norm. We further prove that our scheme is of second-order convergence in space and of first-order convergence in time. Numerical experiments are presented to validate theoretical result.