Many application from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis methods is a suitable means to reduce computational time. In this proceedings, we show the applicability of reduced basis framework to a finite volume scheme of a parametrized and highly non-linear convection-diffusion problem with discontinuous solutions. The complexity of the problem setting requires the use of several new techniques like parametrized empirical operator interpolation, efficient a posteriori error estimation and adaptive generation of reduced data. These methods and their effects are shortly revised in this presentation and the new adaptive generation of interpolation data is described.

@InProceedings{DHO11,
  author       = {Drohmann, M. and Haasdonk, B. and Ohlberger, M.},
  title        = {Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations},
  booktitle    = {Finite Volumes for Complex Applications VI - Problems \& Perspectives},
  series       = {Springer Proceedings in Mathematics 4},
  volume       = {1},
  pages        = {369--377},
  year         = {2011},
  editor       = {J. Fort et al.},
  publisher    = {Springer},
  doi          = {10.1007/978-3-642-20671-9_39},
  url          = \{/2011/DHO11},
}