论文信息 - Robust convergence of a compact fourth-order finite difference scheme for reaction–diffusion problems

Robust convergence of a compact fourth-order finite difference scheme for reaction–diffusion problems

We consider a singularly perturbed one-dimensional reaction–diffusion problem with strong layers. The problem is discretized using a compact fourth order finite difference scheme. Altough the discretization is not inverse monotone we are able to establish its maximum-norm stability and to prove its pointwise convergence on a Shishkin mesh. The convergence is uniform with respect to the perturbation parameter. Numerical experiments complement our theoretical results.

Torsten Linß | T. Linß

[1] Lutz Tobiska,et al. Numerical Methods for Singularly Perturbed Differential Equations , 1996 .

[2] Carmelo Clavero,et al. High Order varepsilon-Uniform Methods for Singularly Perturbed Reaction-Diffusion Problems , 2000, NAA.

[3] T. Linss,et al. Maximum-norm error analysis of a non-monotone FEM for a singularly perturbed reaction-diffusion problem , 2007 .

[4] Torsten Linß,et al. Layer‐adapted meshes for time‐dependent reaction‐diffusion problems , 2006 .

[5] Carmelo Clavero,et al. High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems , 2005, Appl. Math. Comput..

[6] Torsten Linß,et al. Layer-adapted meshes for convection-diffusion problems , 2003 .

[7] L. P. Shishkina,et al. FITTED MESH METHODS FOR PROBLEMS WITH PARABOLIC BOUNDARY LAYERS , 1998 .

[8] John J. H. Miller. Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions , 1996 .

[9] Lubin G. Vulkov,et al. High order ε-uniform methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and singular sources , 2004 .