Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions

作者：

Highlights：

• We develop a numerical method for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions.

• We consider a modified Euler scheme in time, a central differencing in space, and a special scheme for Robin boundary conditions.

• The mesh in the space direction is generated via the equidistribution of a suitably chosen monitor function.

• We prove that the method is a parameter-uniformly convergent of order two in space and order one in time.

摘要

•We develop a numerical method for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions.•We consider a modified Euler scheme in time, a central differencing in space, and a special scheme for Robin boundary conditions.•The mesh in the space direction is generated via the equidistribution of a suitably chosen monitor function.•We prove that the method is a parameter-uniformly convergent of order two in space and order one in time.

论文关键词：Boundary layers,Robin boundary conditions,Adaptive mesh,Equidistribution principle

论文评审过程：Received 8 April 2020, Revised 28 July 2020, Accepted 13 September 2020, Available online 10 October 2020, Version of Record 10 October 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125677