Int. J. of Computing Science and Mathematics   »   2009 Vol.2, No.4



Title: Reduced Basis Method for quadratically nonlinear transport equations


Author: N. Jung, B. Haasdonk, D. Kroner


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


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.


Keywords: model reduction; RBM; reduced basis methods; parameter dependent transport equations; time-dependent viscous Burgers equation; a posteriori error estimates; computing science; quadratically nonlinear transport equations; parametrised PDEs; partial differential equations; finite element method; FEM.


DOI: 10.1504/IJCSM.2009.030912


Int. J. of Computing Science and Mathematics, 2009 Vol.2, No.4, pp.334 - 353


Available online: 11 Jan 2010



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