Reduced basis method for quadratically nonlinear transport equations
type: Item
instance of: scholarly article
title: Reduced basis method for quadratically nonlinear transport equations
zbMATH Open document ID: 1189.65225
DOI: 10.1504/IJCSM.2009.030912
author: N. Jung
author: Dietmar Kröner
author: B. Haasdonk
published in: International Journal of Computing Science and Mathematics
publication date: 2010-05-07T00:00:00Z
review text: Summary: If many numerical solutions of parametrised partial differential equations have to be computed for varying parameters, usual finite element methods (FEM) suffer from too high computational costs. The reduced basis method (RBM) allows to solve parametrised problems faster than by a direct FEM. In the current presentation we extend the RBM for the stationary viscous Burgers equation to the time-dependent case and general quadratically nonlinear transport equations. A posteriori error estimators justify the approach. Numerical experiments on a parameter-dependent transport problem demonstrate the applicability of the model reduction technique. Comparison of the CPU times for RBM and FEM demonstrates the efficiency.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K61
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 5705070
zbMATH Keywords: model reduction
zbMATH Keywords: reduced basis methods
zbMATH Keywords: parameter dependent transport equations
zbMATH Keywords: time-dependent viscous Burgers equation
zbMATH Keywords: a posteriori error estimates
zbMATH Keywords: quadratically nonlinear transport equations
zbMATH Keywords: parametrised PDEs
zbMATH Keywords: finite element method
zbMATH Keywords: FEM
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
describes a project that uses: rbMIT
MaRDI profile type: Publication
full work available at URL: ijcsm.2009.030912
OpenAlex ID: W2105323170
description: scientific article; zbMATH DE number 5705070