Adaptive finite element simulation of currents at microelectrodes to a guaranteed accuracy. Theory

In our accompanying paper (K. Harriman et al., Electrochem. Commun. 2 (2000) 150) we demonstrated how, for the finite element method, an automatic mesh-adaptation algorithm can be derived, given an a posteriori error bound on the simulated current. In this paper we give the technical details of the background theory of the finite element method, and the derivation of the a posteriori error bound.