Numerical simulation of diffusion controlled reactions

Abstract

The amperometric response of electrodes generally cannot be predicted without taking into account mass transport effects.  These are described by partial differential equations that often require numerical solution.  In this thesis the adaptive finite element method is examined as a means to this end.

Adaptive finite element, while long used in engineering fields, has not so far been significant in electrochemical simulation.  Most simulations have been effected with obsolescent finite difference or non-adaptive finite element, with a priori mesh densities.  Neither of these has the advantage of error control that the algorithm presented here has, nor do they allow the same geometric flexibility.  An efficient, and in many ways novel, implementation of adaptive finite element is described, which allows a user-defined error bound to be met using an optimised machine-generated mesh.  Rather than utilising generic error measures, the mesh is optimised specifically for accuracy in the current using a new error estimation strategy.  This yields a widely applicable steady state simulation program whose flexibility is demonstrated with a variety of realistic problems.

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