一类具有抛物边界的对流扩散方程的耦合解法

Coupling Method of a Class of Convective Diffusion Equations with Parabolic Boundary

研究一类具有抛物边界的对流扩散方程的局部间断有限元和连续有限元的耦合方法﹒数值实验验证了Shishkin网格下采用双线性元,可以达到关联范数下的一致收敛阶O(lnN/N),数值实验也表明L^2范数下该方法可达到一致收敛阶O((lnN/N)^(3/2))

A coupled approach of local discontinuous Galerkin（LDG） and continuous finite element method（CFEM） is considered for two-dimensional convection-diffusion problems with regular parabolic layers. Numerical experiments show that the uniform convergence rate O（lnN/N） in the associated norm is established when the bilinear element under the Shishkin mesh is used. Moreover, it is observed numerically that the uniform convergence rate O（（lnN/N）^（3/2）） in L^2 norm can be reached and the CFEM-LDG coupled method is slightly superior to the NIPG method and the CFEM-NIPG coupled method.