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

Abstract

We studied the efficiency and accuracy of a general purpose finite element software in the numerical solution of electrochemical models. Typical numerical complications like boundary singularities, stiffness and multiscale problems were addressed. The convergence order was determined for various mesh refinement strategies. As a general rule, the numerical efficiency of the software proved adequate to the problems dealt, but the default generated meshes and the adaptive mesh adjustment do not work properly, if high levels of accuracy are required. Therefore, a manual adjustment of the mesh control parameters is indispensable. A thorough discussion of the problem of adjusting the mesh was presented to serve as a general introduction to the subject for beginners in the field. Additionally, it was suggested a general approach for mesh optimization through which the convergence rate can be considerably increased.