Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type
Numerical Analysis
2023-10-03 v1 Numerical Analysis
Abstract
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform numerical method. These schemes satisfy a discrete maximum principle. In the classical case, the numerical approximations converge, in the maximum pointwise norm, at a rate of second order and the approximations converge at a rate of first order for all values of the singular perturbation parameter.
Cite
@article{arxiv.2310.01237,
title = {Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type},
author = {Alan F. Hegarty and Eugene O'Riordan},
journal= {arXiv preprint arXiv:2310.01237},
year = {2023}
}
Comments
2 figures