Method of lines and direct discretization: A comparison for linear advection
type: Item
instance of: scholarly article
title: Method of lines and direct discretization: A comparison for linear advection
zbMATH Open document ID: 0797.65067
DOI: 10.1016/0168-9274(94)90009-4
author: R. A. Trompert
author: Willem Hundsdorfer
published in: Applied Numerical Mathematics
publication date: 1994-10-09T00:00:00Z
full work available at URL: https://ir.cwi.nl/pub/1464
review text: Two related schemes are compared for two-dimensional linear advection: a scheme based on dimension splitting starting from fully discrete one- dimensional discretization, and a scheme based on the method of lines. Both schemes use the same four-point upwind biased stencil in each direction and both are considered with flux limiting to avoid oscillations and negative values of the solution. Theoretical aspects of the application of the methods for 2-D models involving error analysis and computational cost are discussed. Numerical tests are run on uniform grids with local uniform grid refinement to compare their accuracy and computational efficiency.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 550352
zbMATH Keywords: numerical tests
zbMATH Keywords: linear advection
zbMATH Keywords: dimension splitting
zbMATH Keywords: method of lines
zbMATH Keywords: four-point upwind biased stencil
zbMATH Keywords: error analysis
zbMATH Keywords: grid refinement
zbMATH Keywords: computational efficiency
reviewed by: Roumen Anguelov
MaRDI profile type: Publication
OpenAlex ID: W2123158640
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description: scientific article; zbMATH DE number 550352