Numerical Analysis Group Research Report NA-00/09

Adaptive Finite Element Simulation of Currents at Microelectrodes to a Guaranteed Accuracy. Application to Channel Microband Electrodes.

Kathryn Harriman David Gavaghan Paul Houston David Kay Endre Süli

May 2000, 31 pages

We extend our earlier work (see K. Harriman et al., Technical Report NA99/19) on adaptive finite element methods for disc electrodes to the case of reaction mechanisms to the increasingly popular channel microband electrode configuration. We use the standard Galerkin finite element method for the diffusion-dominated (low-flow) case, and the streamline diffusion finite element method for the convection-dominated (high-flow) case. We first consider the simple E reaction mechanism (convection-diffusion equation) and we demonstrate excellent agreement with previous approximate analytical results across the range of parameters of interest, on comparatively coarse meshes. We then consider ECE and EC₂E reaction mechanisms (linear and nonlinear systems of reaction-convection-diffusion equations, respectively); again we are able to demonstrate excellent agreement with previous results.

The authors are pleased to acknowledge the financial support of the following organisations: a research studentship for KH; a Career Development Fellowship from the Medical Research Council for DJG, which has allowed them to undertake this research.

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