Using the right side of Poisson’s equation to save on numerical calculations in FEM simulation of electrochemical systems

This work justifies using the right side of Poisson’s equation (RSPE)1 to simulate constant potential electrodes (CPEl) in electrochemical processes. These have traditionally been considered in the boundary conditions of the corresponding boundary value problem (BVP), but in some cases working with the RSPE is much more versatile, efficient and suitable. If constant potential regions are considered as boundaries, then the domain constantly changes as the number, size and position of the regions change; but if they are considered as the source term, the domain remains the same, no matter how many electrodes there are or how or where they are located. Some examples will be solved in order to clearly show that the complicated process of redefining a domain mesh and numbering its corresponding nodes in the finite element method (FEM) is sometimes unnecessary when the electrodes are represented with a suitable function on the RSPE. These practical examples are simulated using a finite element program developed by the authors