# Leibniz MMS Days 2023 - Abstract

**Runge, Daniel**

*Mass-conservative reduced basis approach for convection-diffusion equations with non-linear boundary reaction conditions*

This talk presents an efficient strategy to solve advection-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous catalysis. Since the non-linearity only involves the degrees of freedom along (a part of) the boundary, a reduced basis ansatz is suggested that computes discrete basis functions for the present advection-diffusion operator such that the global non-linear problem reduces to a smaller problem on the boundary. The computed basis functions are completely independent of the non-linearities. Thus, they can be reused for problems with the same differential operator and geometry. Corresponding scenarios might be inverse problems, but also modeling the effect of different catalysts in the same reaction chamber. The strategy is explained for a mass-conservative finite volume method and demonstrated in a numerical example implemented in the julia language.