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.
|Journal||Mathematical and Computer Modelling of Dynamical Systems: methods, tools and applications in engineering and related sciences|
|Publication status||Published - 2016|
- a-posteriori error analysis
- Finite volume schemes
- parameter estimation
- POD-greedy algorithm
- reduced-basis method