奇异摄动问题内罚间断有限方法的最优阶一致收敛性分析

AN ANALYSIS OF OPTIMAL ORDER UNIFORMLY CONVERGENT INTERIOR PENALTY DISCONTINUOUS GALERKIN METHODS FOR SINGULARLY PERTURBED PROBLEMS

本文在Bakhvalov-Shishkin网格上分析了采用高次元的内罚间断有限元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,Bakhva,lov-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 interior penalty amcontmuous Calerkin methods on BakhvMov-Shishkin meshes for solving singularly perturbed convection- diffusion problems. Based on piecewise polynomial approximations of degree k ≥ 1, an optimal uniform convergence rate О（N-k） is obtained on Bakhvalov-Shishkin meshes where N is the number of elements. Numerical experiments complement the theoretical results.