Linearly implicit approximations of diffusive relaxation systems
type: Item
instance of: scholarly article
title: Linearly implicit approximations of diffusive relaxation systems
zbMATH Open document ID: 1279.65097
author: Fausto Cavalli
published in: Acta Applicandae Mathematicae
publication date: 2013-06-13T00:00:00Z
review text: This paper deals with the combination of relaxation systems with implicit approximations and its theoretical and numerical stability analysis. The author introduces diffusiv relaxation systems for the linear and nonlinear model and presents a discrete approximation of the linear one. This approach is extended by first- and second-order schemes for the nonlinear case using a linearly implicit method. The scheme is implicit for the relaxation system except for the nonlinear source-term where a suitable linearization technique is used, based on a certain correction term. Several theoretical stability estimates under certain conditions (a constant correction term) are provided for the first- and second-order scheme. Furthermore, some numerical testcases are carried out which confirm the theoretical results and yield good performance also in case of the non-constant correction.
reviewed by: Martina Wirz
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 6175227
zbMATH Keywords: relaxation systems
zbMATH Keywords: finite difference method
zbMATH Keywords: linear implicit method
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s10440-012-9781-4
OpenAlex ID: W2050355174
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DOI: 10.1007/S10440-012-9781-4
description: scientific article; zbMATH DE number 6175227