Vertex-centered linearity-preserving schemes for nonlinear parabolic problems on polygonal grids
type: Item
instance of: scholarly article
title: Vertex-centered linearity-preserving schemes for nonlinear parabolic problems on polygonal grids
zbMATH Open document ID: 1398.65224
author: Jiming Wu
published in: Journal of Scientific Computing
publication date: 2018-03-13T00:00:00Z
review text: A family of vertex-centered finite volume schemes is constructed for the numerical solution of highly nonlinear parabolic equations with applications to radiation hydrodynamics and magneto hydrodynamics. The primary unknowns are defined at the cell vertices and the derivation of the scheme is performed through a linearity preserving approach. The scheme is locally conservative, linearity preserving, coercive on arbitrary polygonal grids with star shaped cells and capable of handling arbitrary discontinuities. Examples are demonstrated on elliptic problems with discontinuities, nonlinear parabolic problem, radiation diffusion problem and spherical nonlinear heat wave; it is shown that the scheme can work well although with low convergence. Several theorems and lemmas are stated and proved.
Mathematics Subject Classification ID: 65M08
zbMATH DE Number: 6849479
zbMATH Keywords: nonlinear parabolic problem
zbMATH Keywords: vertex-centred finite volume scheme
zbMATH Keywords: linearity preserving discretization
describes a project that uses: ICF3D
describes a project that uses: TRHD
MaRDI profile type: Publication
full work available at URL: s10915-016-0309-3
OpenAlex ID: W2531982552
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DOI: 10.1007/S10915-016-0309-3
description: scientific article; zbMATH DE number 6849479