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- Title
An adaptive grid method for a singularly perturbed convection-diffusion equation with a discontinuous convection coefficient.
- Authors
Mai, Xiongfa; Zhu, Ciwen; Liu, Libin
- Abstract
In this paper, an adaptive grid method is put forward to solve a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient. First, this problem is discretized by using an upwind finite difference scheme on an arbitrary nonuniform grid except the fixed jump point. Then, a first-order maximum norm a posterior error estimate is derived. Further, based on this a posteriori error estimation and the mesh equidistribution principle, an adaptive grid generation algorithm is constructed. Finally, some numerical experiments are presented that support our theoretical estimate.
- Subjects
DISCONTINUOUS coefficients; FINITE differences; TRANSPORT equation; DIFFERENTIAL-difference equations
- Publication
Networks & Heterogeneous Media, 2023, Vol 18, Issue 4, p1
- ISSN
1556-1801
- Publication type
Article
- DOI
10.3934/nhm.2023067