New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics
This paper focuses on a new error analysis and a recovering technique of frequently-used mixed FEMs for a dynamical incompressible magnetohydrodynamics (MHD) system. The methods use the standard inf-sup stable Taylor–Hood/MINI velocity-pressure space pairs to solve the Navier–Stokes equations and th...
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| Veröffentlicht in: | Numerische Mathematik 2023-03, Vol.153 (2-3), p.327-358 |
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| creator | Gao, Huadong Qiu, Weifeng Sun, Weiwei |
| description | This paper focuses on a new error analysis and a recovering technique of frequently-used mixed FEMs for a dynamical incompressible magnetohydrodynamics (MHD) system. The methods use the standard inf-sup stable Taylor–Hood/MINI velocity-pressure space pairs to solve the Navier–Stokes equations and the Nédélec’s edge element for solving the magnetic field. We establish new and optimal error estimates. In particular, we prove that the method provides the optimal accuracy for the MINI element in
L
2
-norm and for the Taylor-Hood element in
H
1
-norm. The analysis is based on a modified Maxwell projection and the corresponding estimates in negative norms, while all the existing analysis is not optimal due to the strong coupling of system and the pollution of the lower-order Nédélec’s edge approximation in analysis. In addition, at any given time step, we develop a simple recovery technique for numerical approximation to the magnetic field of one order higher accuracy in the spatial direction. |
| doi_str_mv | 10.1007/s00211-022-01341-9 |
| format | Article |
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L
2
-norm and for the Taylor-Hood element in
H
1
-norm. The analysis is based on a modified Maxwell projection and the corresponding estimates in negative norms, while all the existing analysis is not optimal due to the strong coupling of system and the pollution of the lower-order Nédélec’s edge approximation in analysis. In addition, at any given time step, we develop a simple recovery technique for numerical approximation to the magnetic field of one order higher accuracy in the spatial direction.</description><identifier>ISSN: 0029-599X</identifier><identifier>EISSN: 0945-3245</identifier><identifier>DOI: 10.1007/s00211-022-01341-9</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Approximation ; Error analysis ; Estimates ; Magnetic fields ; Magnetohydrodynamics ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Norms ; Numerical Analysis ; Numerical and Computational Physics ; Simulation ; Theoretical</subject><ispartof>Numerische Mathematik, 2023-03, Vol.153 (2-3), p.327-358</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-ef79d39faad771bdcac8e66b05b2684780ccb242434ef32c761388d5aa7a62a63</citedby><cites>FETCH-LOGICAL-c249t-ef79d39faad771bdcac8e66b05b2684780ccb242434ef32c761388d5aa7a62a63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00211-022-01341-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00211-022-01341-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Gao, Huadong</creatorcontrib><creatorcontrib>Qiu, Weifeng</creatorcontrib><creatorcontrib>Sun, Weiwei</creatorcontrib><title>New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics</title><title>Numerische Mathematik</title><addtitle>Numer. Math</addtitle><description>This paper focuses on a new error analysis and a recovering technique of frequently-used mixed FEMs for a dynamical incompressible magnetohydrodynamics (MHD) system. The methods use the standard inf-sup stable Taylor–Hood/MINI velocity-pressure space pairs to solve the Navier–Stokes equations and the Nédélec’s edge element for solving the magnetic field. We establish new and optimal error estimates. In particular, we prove that the method provides the optimal accuracy for the MINI element in
L
2
-norm and for the Taylor-Hood element in
H
1
-norm. The analysis is based on a modified Maxwell projection and the corresponding estimates in negative norms, while all the existing analysis is not optimal due to the strong coupling of system and the pollution of the lower-order Nédélec’s edge approximation in analysis. In addition, at any given time step, we develop a simple recovery technique for numerical approximation to the magnetic field of one order higher accuracy in the spatial direction.</description><subject>Approximation</subject><subject>Error analysis</subject><subject>Estimates</subject><subject>Magnetic fields</subject><subject>Magnetohydrodynamics</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Norms</subject><subject>Numerical Analysis</subject><subject>Numerical and Computational Physics</subject><subject>Simulation</subject><subject>Theoretical</subject><issn>0029-599X</issn><issn>0945-3245</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAURS0EEqXwB5gsMRv8lTgeUdUCUoEFJDbLceySKomLXyrIvyeQSmxM7w7nXukdhC4ZvWaUqhuglDNGKOeEMiEZ0UdoRrXMiOAyOx4z5ZpkWr-dojOALaVM5ZLN0PrJf2Lb2WaAGnAMuK2_fIVXy0fAISZcDZ1ta2cbXHcutrvkAeqy8bi1m8738X2oUjxAcI5Ogm3AXxzuHL2uli-Le7J-vntY3K6J41L3xAelK6GDtZVSrKycdYXP85JmJc8LqQrqXMkll0L6ILhTORNFUWXWKptzm4s5upp2dyl-7D30Zhv3aXwCDFdFxiWTTIwUnyiXIkDywexS3do0GEbNjzUzWTOjNfNrzeixJKYSjHC38elv-p_WN9ZQcEQ</recordid><startdate>20230301</startdate><enddate>20230301</enddate><creator>Gao, Huadong</creator><creator>Qiu, Weifeng</creator><creator>Sun, Weiwei</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230301</creationdate><title>New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics</title><author>Gao, Huadong ; Qiu, Weifeng ; Sun, Weiwei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-ef79d39faad771bdcac8e66b05b2684780ccb242434ef32c761388d5aa7a62a63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Approximation</topic><topic>Error analysis</topic><topic>Estimates</topic><topic>Magnetic fields</topic><topic>Magnetohydrodynamics</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Norms</topic><topic>Numerical Analysis</topic><topic>Numerical and Computational Physics</topic><topic>Simulation</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gao, Huadong</creatorcontrib><creatorcontrib>Qiu, Weifeng</creatorcontrib><creatorcontrib>Sun, Weiwei</creatorcontrib><collection>CrossRef</collection><jtitle>Numerische Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gao, Huadong</au><au>Qiu, Weifeng</au><au>Sun, Weiwei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics</atitle><jtitle>Numerische Mathematik</jtitle><stitle>Numer. Math</stitle><date>2023-03-01</date><risdate>2023</risdate><volume>153</volume><issue>2-3</issue><spage>327</spage><epage>358</epage><pages>327-358</pages><issn>0029-599X</issn><eissn>0945-3245</eissn><abstract>This paper focuses on a new error analysis and a recovering technique of frequently-used mixed FEMs for a dynamical incompressible magnetohydrodynamics (MHD) system. The methods use the standard inf-sup stable Taylor–Hood/MINI velocity-pressure space pairs to solve the Navier–Stokes equations and the Nédélec’s edge element for solving the magnetic field. We establish new and optimal error estimates. In particular, we prove that the method provides the optimal accuracy for the MINI element in
L
2
-norm and for the Taylor-Hood element in
H
1
-norm. The analysis is based on a modified Maxwell projection and the corresponding estimates in negative norms, while all the existing analysis is not optimal due to the strong coupling of system and the pollution of the lower-order Nédélec’s edge approximation in analysis. In addition, at any given time step, we develop a simple recovery technique for numerical approximation to the magnetic field of one order higher accuracy in the spatial direction.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00211-022-01341-9</doi><tpages>32</tpages></addata></record> |
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| subjects | Approximation Error analysis Estimates Magnetic fields Magnetohydrodynamics Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Norms Numerical Analysis Numerical and Computational Physics Simulation Theoretical |
| title | New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics |
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