Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations

Drohmann M, Haasdonk B, Ohlberger M

Abstract

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.