POD Galerkin Schemes for Nonlinear Elliptic-Parabolic Systems

In this paper the authors study a nonlinear elliptic-parabolic system, which is motivated by mathematical models for lithium ion batteries. For the reliable and fast numerical solution of the system a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The strategy is justified by an a-priori error estimate for the error between the solution to the coupled system and its POD approximation. The nonlinear coupling is realized by variants of the empirical interpolation introduced by Barrault et al. [3] and Chaturantabut et al. [4]. Numerical examples illustrate the efficiency of the proposed reduced-order modeling.