A Viscosity-Independent Error Estimate of a Pressure-Stabilized Lagrange–Galerkin Scheme for the Oseen Problem
We consider a pressure-stabilized Lagrange–Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order k for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the veloci...
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| Veröffentlicht in: | Journal of scientific computing 2019-08, Vol.80 (2), p.834-858 |
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| creator | Uchiumi, Shinya |
| description | We consider a pressure-stabilized Lagrange–Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order
k
for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the velocity with a constant independent of the viscosity if the exact solution is sufficiently smooth. We also show an error estimate of a discrete primitive of the pressure. Numerical examples show high accuracy of the scheme for problems with small viscosity. |
| doi_str_mv | 10.1007/s10915-019-00958-7 |
| format | Article |
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k
for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the velocity with a constant independent of the viscosity if the exact solution is sufficiently smooth. We also show an error estimate of a discrete primitive of the pressure. Numerical examples show high accuracy of the scheme for problems with small viscosity.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-019-00958-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Approximation ; Computational Mathematics and Numerical Analysis ; Errors ; Exact solutions ; Finite element analysis ; Galerkin method ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Ordinary differential equations ; Theoretical ; Velocity ; Viscosity</subject><ispartof>Journal of scientific computing, 2019-08, Vol.80 (2), p.834-858</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c385t-e2a77d96ccffd563a15465eac6fdb2e6673a7461e7ad6162e0dc40e41f45c81e3</citedby><cites>FETCH-LOGICAL-c385t-e2a77d96ccffd563a15465eac6fdb2e6673a7461e7ad6162e0dc40e41f45c81e3</cites><orcidid>0000-0003-1042-0001</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10915-019-00958-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918315456?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21367,27901,27902,33721,41464,42533,43781,51294</link.rule.ids></links><search><creatorcontrib>Uchiumi, Shinya</creatorcontrib><title>A Viscosity-Independent Error Estimate of a Pressure-Stabilized Lagrange–Galerkin Scheme for the Oseen Problem</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>We consider a pressure-stabilized Lagrange–Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order
k
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k
for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the velocity with a constant independent of the viscosity if the exact solution is sufficiently smooth. We also show an error estimate of a discrete primitive of the pressure. Numerical examples show high accuracy of the scheme for problems with small viscosity.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-019-00958-7</doi><tpages>25</tpages><orcidid>https://orcid.org/0000-0003-1042-0001</orcidid></addata></record> |
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| ispartof | Journal of scientific computing, 2019-08, Vol.80 (2), p.834-858 |
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| subjects | Algorithms Approximation Computational Mathematics and Numerical Analysis Errors Exact solutions Finite element analysis Galerkin method Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Ordinary differential equations Theoretical Velocity Viscosity |
| title | A Viscosity-Independent Error Estimate of a Pressure-Stabilized Lagrange–Galerkin Scheme for the Oseen Problem |
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