带间断系数的奇异摄动对流扩散方程的自适应移动网格方法

Adaptive grid methods for a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient

文中研究了一类带间断系数的奇异摄动对流扩散方程的自适应移动网格算法.首先,给出了连续解及其导数的估计.在任意网格下建立了相应的迎风有限差分格式,并给出了相应的先验误差估计.然后,基于该先验误差估计,设计出一个自适应网格生成算法,并证明了该算法是一阶一致收敛的.最后的数值结果验证了算法的理论结果.

In this paper,adaptive grid methods for a singularly perturbed convection-difusion problem with a discontinuous convection coeficient is considered.Firstly,theoretical bounds on the continuous solutions and derivatives of the solution are derived.A upwind finite difference scheme is constructed on arbitrary mesh,and the corresponding prior error estimates are given.Then,based on the prior error estimation,an adaptive mesh generation algorithm is designed,and it is proved that the algorithm is first-order uniform convergence.Finally,numerical results are presented which support the theoretical results of the algorithm.