EChem++ – An object-oriented problem solving environment for electrochemistry: Part 4. Adaptive multilevel finite elements applied to electrochemical models Algorithm and benchmark calculations

We present an approach for the modeling and simulation of electrochemical processes based on a general mathematical formulation, for which we expect future extensibility. For the numerical solution we propose the Rothe method with adaptive 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 compiler 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.