Abstract
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 in
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11201307
Funding source: Ministry of Education of the People’s Republic of China
Award Identifier / Grant number: 20123127120001
Funding statement: The research of the second author was in part supported by the National Natural Science Foundation of China (11201307) and the Ministry of Education of China through Specialized Research Fund for the Doctoral Program of Higher Education (20123127120001).
Acknowledgements
The authors wish to thank the two referees for their helpful comments and constructive suggestions on the manuscript. The first author would like to thank the Hausdorff Center for Mathematics, University of Bonn, for the generous support, and the Institute for Numerical Simulation, University of Bonn, for the kind host.
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