Adaptive Multilevel Finite Elements Applied to Electrochemical Models Algorithm and Benchmark Calculations ⋆

We present an approach for the modeling and simulation of electrochemical pro-cesses based on a general mathematical formulation, for which we expect future extensibility. For the numerical solution we propose the Rothe method with adap-tive time integration performed by Rosenbrock schemes. For spatial integration we choose an adaptive finite element algorithm, controlled by a hierarchical a posteriori error estimator. The algorithm is designed to simulate models of potential-controlled transient experiments in 1D cell geometries and diffusional transport. It is tested for cyclic voltammetry with a fast electron transfer under semi-infinite diffusion conditions. Results of selected Rosenbrock methods are compared. We discuss the software design of the algorithm, as well as its coupling to the electrochemical com-piler Ecco within an object-oriented framework. The software developed within this study is part of EChem++ and can be obtained freely as open-source code