奇异摄动问题FEM/LDG耦合方法的最优阶一致收敛性分析

UNIFORMLY CONVERGENT HIGHER ORDER FEM/LDG COUPLED METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEM ON BAKHVALOV-SHISHKIN MESH

本文在Bakhvalov-Shishkin网格上分析了采用高次元的FEM/LDG耦合方法求解一维对流扩散型奇异摄动问题的最优阶一致收敛性.取k(k≥1)次分片多项式和网格剖分单元数为N时,在能量范数度量下,Bakhvalov-Shishkin网格上可获得O(N^(-k))的一致误差估计.在数值算例部分对理论分析结果进行了验证.

In this paper, we propose and analyze a higher order FEM/LDG coupled method for solving singularly perturbed convection-diffusion problem. Based on piecewise polynomial approximations of degree k（k ≥ 1）, a uniform convergence rate （9（N-k） in associated norm is established on Bakhvalov-Shishkin mesh, where N is the number of elements. Numerical experiments complement the theoretical results.