A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem
We study a posteriori error analysis of the virtual element method (VEM) for a simplified friction problem, which is a representative elliptic variational inequality of the second kind. By treating hanging nodes as vertices of polygonal elements, the virtual element method does not require any local...
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| Veröffentlicht in: | Journal of scientific computing 2020-06, Vol.83 (3), p.52, Article 52 |
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| creator | Deng, Yanling Wang, Fei Wei, Huayi |
| description | We study a posteriori error analysis of the virtual element method (VEM) for a simplified friction problem, which is a representative elliptic variational inequality of the second kind. By treating hanging nodes as vertices of polygonal elements, the virtual element method does not require any local mesh post-processing after the adaptive mesh refinement. In this work, residual type error estimators are derived for designing adaptive VEM to solve the simplified friction problem. Furthermore, the reliability and efficiency of the error estimators are proved. Finally, a numerical example is given to verify the theoretical results. |
| doi_str_mv | 10.1007/s10915-020-01242-9 |
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Finally, a numerical example is given to verify the theoretical results.</description><subject>Algorithms</subject><subject>Apexes</subject><subject>Approximation</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Error analysis</subject><subject>Estimators</subject><subject>Friction</subject><subject>Grid refinement (mathematics)</subject><subject>Interfaces</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial differential equations</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kEtLAzEUhYMoWKt_wFXAdTSPmcxkWcpUhYoFH7gLmfRGU6aTmqQL_71TR3Dn6m6-cw73Q-iS0WtGaXWTGFWsJJRTQhkvOFFHaMLKSpBKKnaMJrSuS1IVVXGKzlLaUEpVrfgEvc3wKqQM0YfocRNjiLhJ2W9NhoSDw68-5r3pcNPBFvqMHyB_hDV2A2fwk9_uOu88rPEiept96PEqhnZgz9GJM12Ci987RS-L5nl-R5aPt_fz2ZJYwVQmpRFtq8A511onOOXOSkFr13IwUkgpjeMWBLeGybaQRhjrwAhXMluDkEpM0dXYu4vhcw8p603Yx36Y1FyxWrCiZAeKj5SNIaUITu_i8GP80ozqg0E9GtSDQf1jUB9CYgylAe7fIf5V_5P6BroCdLg</recordid><startdate>20200601</startdate><enddate>20200601</enddate><creator>Deng, Yanling</creator><creator>Wang, Fei</creator><creator>Wei, Huayi</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0002-9745-1195</orcidid></search><sort><creationdate>20200601</creationdate><title>A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem</title><author>Deng, Yanling ; 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| subjects | Algorithms Apexes Approximation Computational Mathematics and Numerical Analysis Error analysis Estimators Friction Grid refinement (mathematics) Interfaces Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Partial differential equations Theoretical |
| title | A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem |
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