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ABSTRACT
In this paper, the authors consider a parametrized non-linear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite volume discretization leads to a high-dimensional discrete non-linear problem so that simulation of the parametrized problem for various different parameters is very costly. Therefore, the reduced-basis method is applied, so that the number of degrees of freedom is reduced significantly and a fast numerical simulation of the model is possible. To control the error, an a-posteriori error estimator is derived. Numerical experiments show the efficiency of the approach.
Acknowledgement
The authors gratefully acknowledge partial financial support by the project Reduced Basis Methods for Model Reduction and Sensitivity Analysis of Complex Partial Differential Equations with Applications to Lithium-Ion Batteries funded by the company Adam Opel AG.
Disclosure statement
No potential conflict of interest was reported by the authors.