The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L ∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.

To better understand the nickel-iron electrodeposition process, we have developed one-dimensional numerical model. This model addresses dissociation, diffusion, electromigration, convection and deposition of multiple ion species. The reaction mechanism in this model differs in that N i 2+ and F e 2+ are the electroactive species and N iOH + and F eOH + are not involved whatsover. To take account of the anisotropic behaviour of the solution we introduce a domain decomposition numerical method. Simulations with experimental data shows that our model can predict characteristic features of the nickel-iron system.

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