Convergence of lowest-order semi-Lagrangian schemes
type: Item
instance of: scholarly article
title: Convergence of lowest-order semi-Lagrangian schemes
zbMATH Open document ID: 1273.65121
author: Holger Heumann
author: Ralf Hiptmair
published in: Foundations of Computational Mathematics
publication date: 2013-06-14T00:00:00Z
review text: The authors consider a non-stationary advection-diffusion problem for time-dependent differential forms. By means of the Hille-Yosida theorem, the existence and the uniqueness of the transient advection-diffusion problem are obtained. The semi-Lagrangian Galerkin time-stepping scheme for the considered advection-diffusion problem is presented. Under some additional assumptions, an \(L^2\)-estimate of order \(O(\tau+h^r+h^{r+1}\tau^{-1/2}+\tau^{1/2})\) is established, with \(h\) the spatial meshsize, \(\tau\) the time step and \(r\) the polynomial degree of the trial functions.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M25
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 6176100
zbMATH Keywords: convergence
zbMATH Keywords: advection-diffusion problem
zbMATH Keywords: discrete differential forms
zbMATH Keywords: semi-Lagrangian methods
zbMATH Keywords: error estimate
MaRDI profile type: Publication
full work available at URL: s10208-012-9139-3
OpenAlex ID: W2002752633
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Convergence of lowest-order semi-Lagrangian schemes (DOI)
DOI: 10.1007/S10208-012-9139-3