A Convergent Adaptive Finite Element Method for Cathodic Protection

What is it about?

In this work, we propose and analyze an adaptive finite element method for a steady-state diffusion equation with a nonlinear boundary condition arising in cathodic protection. Under a general assumption on the marking strategy, we show that the algorithm generates a sequence of discrete solutions that converges strongly to the exact solution and the sequence of error estimators has a vanishing limit. Numerical results show clearly the convergence and efficiency of the adaptive algorithm.

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