Split characteristic mixed finite element methods for advection-dominated diffusion equation
ZHANG Jian-song1, ZHANG Yue-zhi1, ZHU Jiang2, YANG Dan-ping3
1. Department of Applied Mathematics, China University of Petroleum, Qingdao 266580, China
2. Laboratorio Nacional de Computa?cao Cient?fica, 25651-075 Petropolis, RJ, Brazil
3. Department of Mathematics, East China Normal University, Shanghai 200062, China
Abstract A split modified method of characteristics mixed finite element (SMMOC-MFE) and a split modified method of characteristics with adjusted advection mixed finite element (SMMOCAA-MFE) are proposed for solving advection-dominated diffusion equations, in which the mixed element systems are symmetric positive definite, and the original variable $u$ and the diffusive flux $\bm\sigma=-\varepsilon\nabla u$ can be solved separately. The optimal-order error estimates in weighted energy norm are derived and some numerical implementations are given to confirm the convergence results.
ZHANG Jian-song, ZHANG Yue-zhi, ZHU Jiang, YANG Dan-ping. Split characteristic mixed finite element methods for advection-dominated diffusion equation. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 338-350.
