Accurate gradient computations at interfaces using finite element methods

International Journal of Applied Mathematics and Computer Science

Ma Zhijie¹  Wang Zhaohui²  Li Zhilin²  Qin Fangfang³ 

[1] College of Resource and Environment, Wuhan University of Technology, Wuhan, 430070China;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of America;School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, 210023China;

关键词: elliptic interface problems;    gradient/flux computation;    ifem;    mixed fe formulation;    computational tube;   

DOI  :  10.1515/amcs-2017-0037

来源: DOAJ

【 摘 要 】

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is to get not only an accurate solution, but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea of Wheeler (1974). For 2D interface problems, the point is to introduce a small tube near the interface and propose the gradient as part of unknowns, which is similar to a mixed finite element method, but only at the interface. Thus the computational cost is just slightly higher than in the standard finite element method. We present a rigorous one dimensional analysis, which shows a second order convergence order for both the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface.

【 授权许可】

Unknown