UNIFORM CONVERGENCE OF A COUPLED METHOD FOR CONVECTION-DIFFUSION PROBLEMS IN 2-D SHISHKIN MESH

作者：Xie, Ziqing; Zhu, Peng^*; Zhou, Shuzi

来源：International Journal of Numerical Analysis and Modeling, 2013, 10(4): 845-859.

• convection diffusion equation
• local discontinuous Galerkin method
• finite element method
• Shishkin mesh
• uniform convergence

In this paper, we introduce a coupled approach of local discontinuous Galerkin (LDG) and continuous finite element method (CFEM) for solving singularly perturbed convection-diffusion problems. When the coupled continuous-discontinuous linear FEM is used under the Shishkin mesh, a uniform convergence rate O(N-1 ln N) in an associated norm is established, where N is the number of elements. Numerical experiments complement the theoretical results. Moreover, a uniform convergence rate O(N-2) in L-2 norm, is observed numerically on the Shishkin mesh.

• 出版日期2013
• 单位湖南师范大学; 湖南大学; 嘉兴学院; 贵州师范大学