Jung, N.; Haasdonk, B.; Kröner, Dietmar B. Reduced basis method for quadratically nonlinear transport equations. (English) Zbl 1189.65225 Int. J. Comput. Sci. Math. 2, No. 4, 334-353 (2009). 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. Cited in 5 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 35Q53 KdV equations (Korteweg-de Vries equations) 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:model reduction; reduced basis methods; parameter dependent transport equations; time-dependent viscous Burgers equation; a posteriori error estimates; quadratically nonlinear transport equations; parametrised PDEs; finite element method; FEM; convergence; numerical experiments Software:rbMIT PDFBibTeX XMLCite \textit{N. Jung} et al., Int. J. Comput. Sci. Math. 2, No. 4, 334--353 (2009; Zbl 1189.65225) Full Text: DOI