| Issue |
ESAIM: M2AN
Volume 53, Number 5, September-October 2019
|
|
|---|---|---|
| Page(s) | 1645 - 1665 | |
| DOI | https://doi.org/10.1051/m2an/2019031 | |
| Published online | 12 August 2019 | |
Article
Quasi-optimality of an Adaptive Finite Element Method for Cathodic Protection
1
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
2
Department of Mathematics and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, 200234 Shanghai, PR China
* Corresponding author: yfxu@shnu.edu.cn, yfxuma@aliyun.com
Received:
16
March
2018
Accepted:
25
April
2019
In this work, we derive a reliable and efficient residual-typed error estimator for the finite element approximation of a 2D cathodic protection problem governed by a steady-state diffusion equation with a nonlinear boundary condition. We propose a standard adaptive finite element method involving the Dörfler marking and a minimal refinement without the interior node property. Furthermore, we establish the contraction property of this adaptive algorithm in terms of the sum of the energy error and the scaled estimator. This essentially allows for a quasi-optimal convergence rate in terms of the number of elements over the underlying triangulation. Numerical experiments are provided to confirm this quasi-optimality.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 65N50 / 35J65
Key words: Cathodic protection / nonlinear boundary condition / a posteriori error estimator / adaptive finite element method / quasi-optimality
© EDP Sciences, SMAI 2019
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