The Mathematical Institute, University of Oxford, Eprints Archive

Adaptive Finite Element Simulation of Steady State Currents at Microdisc Electrodes to a Guaranteed Accuracy

Harriman, Kathryn and Gavaghan, D. J. and Houston, P. and Suli, Endre (1999) Adaptive Finite Element Simulation of Steady State Currents at Microdisc Electrodes to a Guaranteed Accuracy. Technical Report. Unspecified. (Submitted)

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Abstract

We consider the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the "edge-effect". Our approach to overcoming this problem involves the derivation of an a posteriori bound on the error in the numerical approximation for the current which can be used to drive an adaptive mesh-generation algorithm. This allows us to calculate the current to within a prescribed tolerance. Here we demonstrate the power of the method for a simple model problem -- an E reaction mechanism at a microdisc electrode -- for which the analytical solution is known, then we extend the work to the case of a (pseudo) first order EC' reaction mechanism at both an inlaid and a recessed disc.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1282
Deposited By:Lotti Ekert
Deposited On:01 Jun 2011 09:20
Last Modified:01 Jun 2011 09:20

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