APPROXIMATION OF AXISYMMETRIC DARCY FLOW USING MIXED FINITE ELEMENT METHODS
In this article we investigate the numerical approximation of the Darcy equations in an axisymmetric domain, subject to axisymmetric data, using mixed finite element methods. Rewriting the problem in cylindrical coordinates reduces the three-dimensional problem to a problem in two dimensions. This r...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2013-01, Vol.51 (3), p.1421-1442 |
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| creator | ERVIN, V. J. |
| description | In this article we investigate the numerical approximation of the Darcy equations in an axisymmetric domain, subject to axisymmetric data, using mixed finite element methods. Rewriting the problem in cylindrical coordinates reduces the three-dimensional problem to a problem in two dimensions. This reduction to two dimensions requires the numerical analysis to be studied in suitably weighted Hubert spaces. In this setting the Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) approximation pairs are shown to be LBB stable and corresponding a priori error estimates are derived. Presented numerical experiments confirm the predicted rates of convergence for the RT and BDM approximations. |
| doi_str_mv | 10.1137/120861631 |
| format | Article |
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Presented numerical experiments confirm the predicted rates of convergence for the RT and BDM approximations.</description><subject>A priori knowledge</subject><subject>Airy equation</subject><subject>Applied mathematics</subject><subject>Approximation</subject><subject>Axisymmetric</subject><subject>Convergence</subject><subject>Estimates</subject><subject>Finite element method</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Mathematical domains</subject><subject>Mathematical problems</subject><subject>Numerical analysis</subject><subject>Symmetry</subject><subject>Three dimensional</subject><subject>Two dimensional</subject><subject>Uniqueness</subject><subject>Velocity</subject><issn>0036-1429</issn><issn>1095-7170</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNpd0E1Lw0AQBuBFFKzVgz9AWPCih-jObpJNjiFN2sV8lDbF9hSSzQZa2qZm24P_3pVKD56GgYdh3hehRyBvAIy_AyWeCy6DKzQA4jsWB06u0YAQ5lpgU_8W3Wm9IWb3gA3QRzCdzvKlSINC5BnOYxwsxXyVplExEyEeBbNwheMk_8SLucjGOBXLaIRjkYkiwlESpVFWYIMn-Wh-j27aaqvVw98cokUcFeHESvKxCIPEkgzo0WqryiWUkKZVwJtKElfKljLuKuZwj9ZUKbvmSrYtp7KuGQPuN6zxfUo4NZHYEL2c7x767uuk9LHcrbVU2221V91Jl8BcBxxOgBj6_I9uulO_N98ZZXtATV3MqNezkn2nda_a8tCvd1X_XQIpf2stL7Ua-3S2G33s-gu0TSCbgM9-AK6Oapo</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>ERVIN, V. 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| subjects | A priori knowledge Airy equation Applied mathematics Approximation Axisymmetric Convergence Estimates Finite element method Interpolation Mathematical analysis Mathematical domains Mathematical problems Numerical analysis Symmetry Three dimensional Two dimensional Uniqueness Velocity |
| title | APPROXIMATION OF AXISYMMETRIC DARCY FLOW USING MIXED FINITE ELEMENT METHODS |
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