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- Publisher Website: 10.1051/m2an/2019031
- Scopus: eid_2-s2.0-85103486044
- WOS: WOS:000480470700002
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Article: Quasi-Optimality of an Adaptive Finite Element Method for Cathodic Protection
| Title | Quasi-Optimality of an Adaptive Finite Element Method for Cathodic Protection |
|---|---|
| Authors | |
| Keywords | A posteriori error estimator Adaptive finite element method Cathodic protection Nonlinear boundary condition Quasi-optimality |
| Issue Date | 12-Aug-2019 |
| Publisher | EDP Sciences |
| Citation | ESAIM: Mathematical Modelling and Numerical Analysis, 2019, v. 53, n. 5, p. 1645-1665 How to Cite? |
| 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. |
| Persistent Identifier | http://hdl.handle.net/10722/337533 |
| ISSN | 2023 Impact Factor: 2.1 2023 SCImago Journal Rankings: 1.247 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Li, Guanglian | - |
| dc.contributor.author | Xu, Yifeng | - |
| dc.date.accessioned | 2024-03-11T10:21:38Z | - |
| dc.date.available | 2024-03-11T10:21:38Z | - |
| dc.date.issued | 2019-08-12 | - |
| dc.identifier.citation | ESAIM: Mathematical Modelling and Numerical Analysis, 2019, v. 53, n. 5, p. 1645-1665 | - |
| dc.identifier.issn | 2822-7840 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/337533 | - |
| dc.description.abstract | <p>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.<br></p> | - |
| dc.language | eng | - |
| dc.publisher | EDP Sciences | - |
| dc.relation.ispartof | ESAIM: Mathematical Modelling and Numerical Analysis | - |
| dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
| dc.subject | A posteriori error estimator | - |
| dc.subject | Adaptive finite element method | - |
| dc.subject | Cathodic protection | - |
| dc.subject | Nonlinear boundary condition | - |
| dc.subject | Quasi-optimality | - |
| dc.title | Quasi-Optimality of an Adaptive Finite Element Method for Cathodic Protection | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.1051/m2an/2019031 | - |
| dc.identifier.scopus | eid_2-s2.0-85103486044 | - |
| dc.identifier.volume | 53 | - |
| dc.identifier.issue | 5 | - |
| dc.identifier.spage | 1645 | - |
| dc.identifier.epage | 1665 | - |
| dc.identifier.eissn | 2804-7214 | - |
| dc.identifier.isi | WOS:000480470700002 | - |