Reduced Basis Method for quadratically nonlinear transport equations

Authors:
N. Jung;B. Haasdonk;D. Kroner
Affiliations:
Lehrstuhl fur Regelungstechnik, Technische Universitat Munchen, Boltzmannstrasse 15, Garching 85748, Germany.;Institut fur Angewandte Analysis und Numerische Simulation, Universitat Stuttgart, Pfaffenwaldring 57, Stuttgart 70569, Germany.;Abteilung fur Angewandte Mathematik, Albert-Ludwigs-Universitat Freiburg, Hermann-Herder-Str. 10, Freiburg 79104, Germany
Venue:
International Journal of Computing Science and Mathematics
Year:
2009

Citing 2
Cited 0

A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE

Computing
Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 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.