EChem++ – An object-oriented problem solving environment for electrochemistry. Part 5. A differential-algebraic approach to the error control of adaptive algorithms

Adaptive algorithms promise to provide general tools for the solution of dynamic electrochemical simulation models. We describe a modeling strategy which enables an adaptive step size selection in time based on the control of errors in the concentrations both of dissolved and adsorbed molecules and additionally in the electrochemical response, e.g. the current. Combined with automatic finite element grid adaption in space, a robust algorithm is obtained and included in the EChem++ problem solving environment. Simulations of chronoamperometric and cyclic voltammetric experiments in a one-dimensional cell geometry under linear diffusion conditions demonstrate the applicability of the approach. Provisions to integrate potential jumps in the time step control enable a flexible handling of multi-pulse chronoamperometry. Further applications include fast and slow kinetic adsorption processes and those including surface reactions.