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Mathematics > Numerical Analysis

arXiv:1803.06222 (math)
[Submitted on 16 Mar 2018]

Title:Quasi-Optimality of an Adaptive Finite Element Method for Cathodic Protection

Authors:Guanglian Li, Yifeng Xu
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Abstract: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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1803.06222 [math.NA]
  (or arXiv:1803.06222v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1803.06222
Journal reference: ESAIM: Mathematical Modelling and Numerical Analysis, 2019
Related DOI: https://doi.org/10.1051/m2an/2019031

Submission history

From: Guanglian Li [view email]
[v1] Fri, 16 Mar 2018 13:35:40 UTC (176 KB)
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