First-order system least-squares finite element method for singularly perturbed Darcy equations
We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable from the system. It can be recovered by a simple post-process...
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| Veröffentlicht in: | ESAIM. Mathematical modelling and numerical analysis 2023-07, Vol.57 (4), p.2283-2300 |
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| container_title | ESAIM. Mathematical modelling and numerical analysis |
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| creator | Führer, Thomas Videman, Juha |
| description | We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable from the system. It can be recovered by a simple post-processing. It is shown that the least-squares functional is uniformly equivalent,
i.e.
, independent of the singular perturbation parameter, to a parameter dependent norm. This norm equivalence implies that the least-squares functional evaluated in the discrete solution provides an efficient and reliable a posteriori error estimator. Numerical experiments are presented. |
| doi_str_mv | 10.1051/m2an/2023049 |
| format | Article |
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i.e.
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i.e.
, independent of the singular perturbation parameter, to a parameter dependent norm. This norm equivalence implies that the least-squares functional evaluated in the discrete solution provides an efficient and reliable a posteriori error estimator. Numerical experiments are presented.</description><subject>Approximation</subject><subject>Brinkman model</subject><subject>Darcys law</subject><subject>Equivalence</subject><subject>Finite element analysis</subject><subject>Finite element method</subject><subject>Fluid flow</subject><subject>Least squares</subject><subject>Methods</subject><subject>Numerical analysis</subject><subject>Parameters</subject><subject>Porous media</subject><subject>Porous media flow</subject><subject>Singular perturbation</subject><issn>2822-7840</issn><issn>2804-7214</issn><issn>1290-3841</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNotkE1LAzEQhoMoWGpv_oCAV9fma3eTo1SrQsGLnkM2mdXIfrRJ9rD_3iztaYaX552BB6F7Sp4oKem2Z2bYMsI4EeoKrZgkoqgZFdfLzlhRS0Fu0SZG35CSqEqoslohvfchpmIMDgKOc0zQ4w5MjuJpMgEibv3gE2DooIch4R7S7-hwO2bcDz9TZ0I34yOENIUGHH4xwc4Ycjn5cYh36KY1XYTNZa7R9_71a_deHD7fPnbPh8JyQlNRyoZXjjpBJVNAG2OtlKwyYGsnjbA5sqCIMKXKJBV2YZ1qmeJcqZLzNXo43z2G8TRBTPpvnMKQX2omhaCEqbrO1OOZsmGMMUCrj8H3JsyaEr1Y1ItFfbHI_wFlCWa_</recordid><startdate>20230701</startdate><enddate>20230701</enddate><creator>Führer, Thomas</creator><creator>Videman, Juha</creator><general>EDP Sciences</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-5034-6593</orcidid></search><sort><creationdate>20230701</creationdate><title>First-order system least-squares finite element method for singularly perturbed Darcy equations</title><author>Führer, Thomas ; Videman, Juha</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c301t-58b36d1d41829e1bacc8826aec7d8a4ce1bce904a598b314cd1d4d9f293399533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Approximation</topic><topic>Brinkman model</topic><topic>Darcys law</topic><topic>Equivalence</topic><topic>Finite element analysis</topic><topic>Finite element method</topic><topic>Fluid flow</topic><topic>Least squares</topic><topic>Methods</topic><topic>Numerical analysis</topic><topic>Parameters</topic><topic>Porous media</topic><topic>Porous media flow</topic><topic>Singular perturbation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Führer, Thomas</creatorcontrib><creatorcontrib>Videman, Juha</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>ESAIM. Mathematical modelling and numerical analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Führer, Thomas</au><au>Videman, Juha</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>First-order system least-squares finite element method for singularly perturbed Darcy equations</atitle><jtitle>ESAIM. Mathematical modelling and numerical analysis</jtitle><date>2023-07-01</date><risdate>2023</risdate><volume>57</volume><issue>4</issue><spage>2283</spage><epage>2300</epage><pages>2283-2300</pages><issn>2822-7840</issn><eissn>2804-7214</eissn><eissn>1290-3841</eissn><abstract>We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable from the system. It can be recovered by a simple post-processing. It is shown that the least-squares functional is uniformly equivalent,
i.e.
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| language | eng |
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| source | Alma/SFX Local Collection |
| subjects | Approximation Brinkman model Darcys law Equivalence Finite element analysis Finite element method Fluid flow Least squares Methods Numerical analysis Parameters Porous media Porous media flow Singular perturbation |
| title | First-order system least-squares finite element method for singularly perturbed Darcy equations |
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