Reduced Basis Method for quadratically nonlinear transport equations

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.