Repository: Freie Universität Berlin, Math Department

Reduced Basis Approach for Convection-Diffusion Equations with Non-linear Boundary Reaction Conditions

Matera, S. and Merdon, C. and Runge, D. (2023) Reduced Basis Approach for Convection-Diffusion Equations with Non-linear Boundary Reaction Conditions. In: International Conference on Finite Volumes for Complex Applications, 30 October - 3 November 2023, Strasbourg, France.

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This paper aims at an efficient strategy to solve drift-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 Green’s-like functions for the present drift-diffusion operator such that the global non-linear problem reduces to a smaller non-linear problem for a boundary method. 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 in heterogeneous catalysis 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 on a simple numerical example for catalytic CO oxidation.

Item Type:Conference or Workshop Item (Paper)
Uncontrolled Keywords:Reduced basis Non-linear boundary conditions Finite volume methods
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:3119
Deposited By: Ulrike Eickers
Deposited On:21 Feb 2024 14:21
Last Modified:21 Feb 2024 14:21

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