Implicit solution of hyerbolic equations with space-time adaptivity
type: Item
instance of: scholarly article
title: Implicit solution of hyerbolic equations with space-time adaptivity
zbMATH Open document ID: 0999.65084
DOI: 10.1023/A:1021978304268
author: Stefan Söderberg
author: Alison Ramage
author: Lina Hemmingsson-Frändén
author: Per Lötstedt
published in: BIT
publication date: 2002-11-26T00:00:00Z
review text: The authors use the finite volume method in space and a linear multistep method in time on a structured grid to solve numerically multidimensional scalar hyperbolic differential equations in conservation form. The convergence of the numerical solution to the weak solution as volume and time step go to zero has been proved and the corresponding iteration method is discussed. The adaptive algorithm is implemented for parallel execution and the test numerical results are presented for linear problems and compressible Euler equations. In all cases the algorithm selects a grid and a time step adapted to the solutions of the equations.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1749888
zbMATH Keywords: finite volume method
zbMATH Keywords: linear multistep method
zbMATH Keywords: structured grid
zbMATH Keywords: multidimensional hyperbolic conservation law
zbMATH Keywords: adaptive algorithm
zbMATH Keywords: convergence
zbMATH Keywords: compressible Euler equations.
zbMATH Keywords: parallel computation
zbMATH Keywords: numerical examples
zbMATH Keywords: mesh generation
zbMATH Keywords: weak solution
zbMATH Keywords: iteration method
reviewed by: P. B. Dubovski
MaRDI profile type: Publication
full work available at URL: a:1021978304268
OpenAlex ID: W1587809523
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description: scientific article; zbMATH DE number 1749888