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

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

“…We have recently described [1] a general approach for the mathematical modeling and numerical simulation of electrochemical reaction-diffusion processes in one-dimensional geometries. The adaptive algorithm is based on an error estimation in the concentrations of the species involved in the electrode process.…”

Probing the Numerical Convergence of a Commercial Finite Element Software in Electrochemical Simulations

“…Speiser has developed a dedicated software which enables simulation of any electrochemical kinetic model in planar electrodes. 5 Fisher implemented FEM solutions for stationary 6 and hydrodynamic 7 systems finding results which compare satisfactorily with FDM calculations.…”

“…In general these software are equipped with mesh generators, which allow automatic discretization of domains with any degree of complexity. This is argued as an important advantage of the FEM [5][6][7] over the FDM, once latter is originally conceived for staggered grids and needs some special procedures in order to track irregular domains. 8 Another important advantage of the general purpose packages over manually written codes is that it makes physical base modelling possible, i.e., the model is constructed based only on the physical conception of the problem with a minimum of mathematical expertise.…”

Object-oriented implementation of 3D DC adaptive finite-element method

“…Generally, it included a 3D unstructured mesh generation, a-posterior error estimating, adaptive mesh refinement, and postprocessing procedure, which agreed well with the essence of object-oriented philosophy (OOP). AFEM associated with OOP technique was already studied in potential flow (Akin and Singh, 2002), structural mechanics (Niekamp and Stein, 2002), multiphysics applications (Stewart and Edwards, 2004), electrochemistry (Ludwig and Speiser, 2006), astrophysical fluid dynamics (Rosenberg et al, 2006), and crack propagation (Phongthanapanich and Dechaumphai, 2004), etc.…”