SUPG-based stabilization using a separated representations approach
We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG sc...
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| Veröffentlicht in: | International journal of material forming 2010-04, Vol.3 (Suppl 1), p.883-886 |
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| container_issue | Suppl 1 |
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| container_title | International journal of material forming |
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| creator | González, D. Debeugny, L. Cueto, E. Chinesta, F. Díez, P. Huerta, A. |
| description | We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. Thus it is possible to use the technique of separation of variables in the context of problems of convection-diffusion that will lead to a sequence of problems in 1D where the parameter of stabilization is well known. |
| doi_str_mv | 10.1007/s12289-010-0909-7 |
| format | Article |
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The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. 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Cueto</subject><subject>Numerical methods and algorithms</subject><subject>Processes</subject><subject>Àrees temàtiques de la UPC</subject><issn>1960-6206</issn><issn>1960-6214</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>XX2</sourceid><recordid>eNp9kEFLwzAUx4MoOOY-gLdePUTzkrRZjmPoJhQUdOfwmqZbx2xL0gn66U1XGZ4MPJK8_P4v8CPkFtg9MKYeAnA-15QBo0wzTdUFmYDOGM04yMvzmWXXZBbCnsUluFJcTsjybfO6ogUGVyahx6I-1N_Y122THEPdbBNMguvQYx_fveu8C67pT0BIsOt8i3Z3Q64qPAQ3-92nZPP0-L5c0_xl9bxc5NRKpnoqZCmVYCg0aF0oCZZb7eaqyFwlXapFCtrOMbWlLiVyrAAzkTqLAkqeVaWYkrtx7g4PpvP1B_ov02Jt1ovcDD0m0wzi4E-ILIysDUdrvLPOW-xP9PkyFGeKG9ActPiT8W0I3lXnT4CZQbQZRZso2gyijYoZPmZCZJut82bfHn0TNfwT-gER-H-c</recordid><startdate>20100401</startdate><enddate>20100401</enddate><creator>González, D.</creator><creator>Debeugny, L.</creator><creator>Cueto, E.</creator><creator>Chinesta, F.</creator><creator>Díez, P.</creator><creator>Huerta, A.</creator><general>Springer-Verlag</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>XX2</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-6272-3429</orcidid><orcidid>https://orcid.org/0000-0001-6464-6407</orcidid><orcidid>https://orcid.org/0000-0003-1017-4381</orcidid></search><sort><creationdate>20100401</creationdate><title>SUPG-based stabilization using a separated representations approach</title><author>González, D. ; Debeugny, L. ; Cueto, E. ; Chinesta, F. ; Díez, P. ; Huerta, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c407t-34d4730a39199b741c2c9e87b6ef4e593519c8a5cd9d4a2af1a635eca31d26fd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Anàlisi numèrica</topic><topic>CAE) and Design</topic><topic>Computational Intelligence</topic><topic>Computer-Aided Engineering (CAD</topic><topic>Differential equations, Partial</topic><topic>Elements finits, Mètode dels</topic><topic>Engineering</topic><topic>Engineering Sciences</topic><topic>Equacions diferencials parcials</topic><topic>Finite element method</topic><topic>Machines</topic><topic>Manufacturing</topic><topic>Matemàtiques i estadística</topic><topic>Materials Science</topic><topic>Mechanical Engineering</topic><topic>Mechanics</topic><topic>Mètodes numèrics</topic><topic>New and advanced numerical strategies for material forming: E. Cueto</topic><topic>Numerical methods and algorithms</topic><topic>Processes</topic><topic>Àrees temàtiques de la UPC</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>González, D.</creatorcontrib><creatorcontrib>Debeugny, L.</creatorcontrib><creatorcontrib>Cueto, E.</creatorcontrib><creatorcontrib>Chinesta, F.</creatorcontrib><creatorcontrib>Díez, P.</creatorcontrib><creatorcontrib>Huerta, A.</creatorcontrib><collection>CrossRef</collection><collection>Recercat</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>International journal of material forming</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>González, D.</au><au>Debeugny, L.</au><au>Cueto, E.</au><au>Chinesta, F.</au><au>Díez, P.</au><au>Huerta, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>SUPG-based stabilization using a separated representations approach</atitle><jtitle>International journal of material forming</jtitle><stitle>Int J Mater Form</stitle><date>2010-04-01</date><risdate>2010</risdate><volume>3</volume><issue>Suppl 1</issue><spage>883</spage><epage>886</epage><pages>883-886</pages><issn>1960-6206</issn><eissn>1960-6214</eissn><abstract>We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. 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| subjects | Anàlisi numèrica CAE) and Design Computational Intelligence Computer-Aided Engineering (CAD Differential equations, Partial Elements finits, Mètode dels Engineering Engineering Sciences Equacions diferencials parcials Finite element method Machines Manufacturing Matemàtiques i estadística Materials Science Mechanical Engineering Mechanics Mètodes numèrics New and advanced numerical strategies for material forming: E. Cueto Numerical methods and algorithms Processes Àrees temàtiques de la UPC |
| title | SUPG-based stabilization using a separated representations approach |
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