Steady state simulation of electrode processes with a new error bounded adaptive finite element algorithm

In a series of papers, Harriman et al. [1-5] have presented a reliable means of simulating steady state currents with adaptive finite element. They have demonstrated that multi-step, even non-linear, mechanisms, alongside convection, can be incorporated. However. there is considerable complication in the mathematical approach taken, and it would seem to be limited as it stands to certain types of electrode reaction models - notably those without heterogeneous kinetics or transient effects. In this paper we discuss alternative approaches to error estimation and adaptivity, and present a simpler formulation, capable of simulating systems with heterozeneous kinetics; transient simulations also appear more attainable. We introduce, apparently for the first time in electrochemistry, the use of gradient recovery methods [6] to both error estimation and accurate current calculations. The result is an algorithm with considerably more potential for generalisation, closer to the ideal of an entirely flexible automatic simulation program, capable of dealing with any mechanism or electrode geometry. In tests we find our method to perform more efficiently than that cited above, producing accurate results with simpler meshes in less time. (C) 2003 Elsevier Science B.V. All rights reserved.