Uniform convergent tailored finite point method for advection-diffusion equation with discontinuous, anisotropic and vanishing diffusivity
type: Item
instance of: scholarly article
title: Uniform convergent tailored finite point method for advection-diffusion equation with discontinuous, anisotropic and vanishing diffusivity
zbMATH Open document ID: 1359.65234
author: Min Tang
author: Yi-Hong Wang
published in: Journal of Scientific Computing
publication date: 2017-03-02T00:00:00Z
review text: The authors propose the two tailored finite point method for numerical approximation of solutions to steady state advection-diffusion equations with discontinuous, vanishing diffusivity. The first method deals with the case when the diffusion is aligned with the coordinates, while the second one is concerned with general nonaligned tensor diffusivity. The diffusion tensor and advection coefficient are approximated by piecewise constants which allows to locally express the solution by a linear combination of special solutions to the constant coefficient equations. The authors obtain uniform convergence of the proposed algorithms in the vanishing diffusivity limit, even when the solution exhibits interface and boundary layers. In case when the diffusivity is along the coordinates, it is shown that the positivity and maximum principle hold.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 6690803
zbMATH Keywords: anisotropic diffusion
zbMATH Keywords: tailored finite point method
zbMATH Keywords: interface layer
zbMATH Keywords: boundary layer
zbMATH Keywords: uniform convergence
zbMATH Keywords: steady state advection-diffusion equation
zbMATH Keywords: discontinuous, vanishing diffusivity
zbMATH Keywords: algorithm
zbMATH Keywords: maximum principle
MaRDI profile type: Publication
full work available at URL: s10915-016-0254-1
OpenAlex ID: W2498950006
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DOI: 10.1007/S10915-016-0254-1
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description: scientific article; zbMATH DE number 6690803