Improved error and work estimates for high-order elements
SUMMARY Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements....
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| Veröffentlicht in: | International journal for numerical methods in fluids 2013-08, Vol.72 (11), p.1207-1218 |
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| container_title | International journal for numerical methods in fluids |
| container_volume | 72 |
| creator | Lohner, Rainald |
| description | SUMMARY
Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost. Copyright © 2013 John Wiley & Sons, Ltd.
The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of elements in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost. |
| doi_str_mv | 10.1002/fld.3783 |
| format | Article |
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Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost. Copyright © 2013 John Wiley & Sons, Ltd.
The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of elements in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost.</description><identifier>ISSN: 0271-2091</identifier><identifier>EISSN: 1097-0363</identifier><identifier>DOI: 10.1002/fld.3783</identifier><identifier>CODEN: IJNFDW</identifier><language>eng</language><publisher>Bognor Regis: Blackwell Publishing Ltd</publisher><subject>Accuracy ; CFD ; Computational fluid dynamics ; Demand ; Errors ; Estimates ; finite differences ; finite elements ; Flexibility ; high-order schemes ; Mathematical analysis ; Optimization</subject><ispartof>International journal for numerical methods in fluids, 2013-08, Vol.72 (11), p.1207-1218</ispartof><rights>Copyright © 2013 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3973-37c623f15a0003dcd415c6f607f6e078b140a68cd9651f26fc236ce21051b4963</citedby><cites>FETCH-LOGICAL-c3973-37c623f15a0003dcd415c6f607f6e078b140a68cd9651f26fc236ce21051b4963</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Ffld.3783$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Ffld.3783$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Lohner, Rainald</creatorcontrib><title>Improved error and work estimates for high-order elements</title><title>International journal for numerical methods in fluids</title><addtitle>Int. J. Numer. Meth. Fluids</addtitle><description>SUMMARY
Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost. Copyright © 2013 John Wiley & Sons, Ltd.
The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of elements in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost.</description><subject>Accuracy</subject><subject>CFD</subject><subject>Computational fluid dynamics</subject><subject>Demand</subject><subject>Errors</subject><subject>Estimates</subject><subject>finite differences</subject><subject>finite elements</subject><subject>Flexibility</subject><subject>high-order schemes</subject><subject>Mathematical analysis</subject><subject>Optimization</subject><issn>0271-2091</issn><issn>1097-0363</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp1kFFLwzAUhYMoOKfgTyj44kvnTdImzaObbg6mgkx8DF1647q160w25_69GRNFwacLh49zzj2EnFPoUAB2Zauiw2XGD0iLgpIxcMEPSQuYpDEDRY_JifczAFAs4y2ihvXSNe9YROhc46J8UUSbxs0j9KuyzlfoIxvkafk6jRtXoIuwwhoXK39KjmxeeTz7um3y3L8d9-7i0eNg2LsexYYryWMujWDc0jQPmbwwRUJTI6wAaQWCzCY0gVxkplAipZYJaxgXBhmFlE4SJXibXO59Q8-3dail69IbrKp8gc3aa5qEHCYZ5QG9-IPOmrVbhHaacpWlEhJIfwyNa7x3aPXShVfdVlPQuw112FDvNgxovEc3ZYXbfzndH9385ku_wo9vPndzLSSXqX55GOj7cVeoJ9HVI_4JmBN-6w</recordid><startdate>20130820</startdate><enddate>20130820</enddate><creator>Lohner, Rainald</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QH</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>7UA</scope><scope>8FD</scope><scope>C1K</scope><scope>F1W</scope><scope>FR3</scope><scope>H8D</scope><scope>H96</scope><scope>JQ2</scope><scope>KR7</scope><scope>L.G</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20130820</creationdate><title>Improved error and work estimates for high-order elements</title><author>Lohner, Rainald</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3973-37c623f15a0003dcd415c6f607f6e078b140a68cd9651f26fc236ce21051b4963</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Accuracy</topic><topic>CFD</topic><topic>Computational fluid dynamics</topic><topic>Demand</topic><topic>Errors</topic><topic>Estimates</topic><topic>finite differences</topic><topic>finite elements</topic><topic>Flexibility</topic><topic>high-order schemes</topic><topic>Mathematical analysis</topic><topic>Optimization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lohner, Rainald</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Aqualine</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Water Resources Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>International journal for numerical methods in fluids</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lohner, Rainald</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Improved error and work estimates for high-order elements</atitle><jtitle>International journal for numerical methods in fluids</jtitle><addtitle>Int. J. Numer. Meth. Fluids</addtitle><date>2013-08-20</date><risdate>2013</risdate><volume>72</volume><issue>11</issue><spage>1207</spage><epage>1218</epage><pages>1207-1218</pages><issn>0271-2091</issn><eissn>1097-0363</eissn><coden>IJNFDW</coden><abstract>SUMMARY
Work estimates for high‐order elements are derived. The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of element in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost. Copyright © 2013 John Wiley & Sons, Ltd.
The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher‐order elements. As expected, the estimates also show that the optimal order of elements in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high‐order elements and their finite difference counterparts reveals a work‐ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro‐unstructured grids is worth such a high cost.</abstract><cop>Bognor Regis</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/fld.3783</doi><tpages>12</tpages></addata></record> |
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| issn | 0271-2091 1097-0363 |
| language | eng |
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| subjects | Accuracy CFD Computational fluid dynamics Demand Errors Estimates finite differences finite elements Flexibility high-order schemes Mathematical analysis Optimization |
| title | Improved error and work estimates for high-order elements |
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