Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations
In this article a spectral Galerkin approximation of fractional advection diffusion optimal control problem with state constraint in L2 norm is discussed. The continuous first order optimality condition is derived. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A pr...
Gespeichert in:
| Veröffentlicht in: | Numerical methods for partial differential equations 2022-09, Vol.38 (5), p.1526-1542 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1542 |
|---|---|
| container_issue | 5 |
| container_start_page | 1526 |
| container_title | Numerical methods for partial differential equations |
| container_volume | 38 |
| creator | Wang, Fangyuan Zhou, Zhaojie |
| description | In this article a spectral Galerkin approximation of fractional advection diffusion optimal control problem with state constraint in L2 norm is discussed. The continuous first order optimality condition is derived. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for state, adjoint state, and control variables in Hα/2 and weighted L2 norms are derived. Numerical examples are presented to verify the theoretical findings. |
| doi_str_mv | 10.1002/num.22853 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2688834126</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2688834126</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2573-a21bdbf697d45d046fb8df964ad89473b7b9b47435113a204c58f5def8dc1c253</originalsourceid><addsrcrecordid>eNp1kLFOwzAURS0EEqUw8AeWmBjS2o6T2COqoCAVGKASm-XEtkhJ49R2qLrxCXwjX4LbsDK9q6vzrt67AFxiNMEIkWnbryeEsCw9AiOMOEsIJfkxGKGC8gRn_O0UnHm_QgjjDPMR2L50ugpONnAuG-0-6haudXi3ChrroA8yaFjZ1kekbrWCtgv1OtLRC8420BponKxCbdvoSvWpD_rn61vVxvR-0E4PCNSbXu6FPwcnRjZeX_zNMVje3b7O7pPF8_xhdrNIKpIVaSIJLlVpcl4omilEc1MyZXhOpWKcFmlZlLykBU0zjFNJEK0yZjKlDVMVjhHpGFwNuZ2zm177IFa2d_FWL0jOGEspJnmkrgeqctZ7p43oXHzT7QRGYt-riL2KQ6-RnQ7stm707n9QPC0fh41fNEJ_AA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2688834126</pqid></control><display><type>article</type><title>Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations</title><source>Wiley Journals</source><creator>Wang, Fangyuan ; Zhou, Zhaojie</creator><creatorcontrib>Wang, Fangyuan ; Zhou, Zhaojie</creatorcontrib><description>In this article a spectral Galerkin approximation of fractional advection diffusion optimal control problem with state constraint in L2 norm is discussed. The continuous first order optimality condition is derived. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for state, adjoint state, and control variables in Hα/2 and weighted L2 norms are derived. Numerical examples are presented to verify the theoretical findings.</description><identifier>ISSN: 0749-159X</identifier><identifier>EISSN: 1098-2426</identifier><identifier>DOI: 10.1002/num.22853</identifier><language>eng</language><publisher>Hoboken, USA: John Wiley & Sons, Inc</publisher><subject>a priori error estimate ; Advection ; Constraints ; fractional advection diffusion reaction equation ; Galerkin method ; Norms ; Optimal control ; optimal control problem ; Optimization ; Polynomials ; spectral Galerkin method</subject><ispartof>Numerical methods for partial differential equations, 2022-09, Vol.38 (5), p.1526-1542</ispartof><rights>2021 Wiley Periodicals LLC.</rights><rights>2022 Wiley Periodicals LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2573-a21bdbf697d45d046fb8df964ad89473b7b9b47435113a204c58f5def8dc1c253</cites><orcidid>0000-0003-0499-1545</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnum.22853$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnum.22853$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Wang, Fangyuan</creatorcontrib><creatorcontrib>Zhou, Zhaojie</creatorcontrib><title>Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations</title><title>Numerical methods for partial differential equations</title><description>In this article a spectral Galerkin approximation of fractional advection diffusion optimal control problem with state constraint in L2 norm is discussed. The continuous first order optimality condition is derived. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for state, adjoint state, and control variables in Hα/2 and weighted L2 norms are derived. Numerical examples are presented to verify the theoretical findings.</description><subject>a priori error estimate</subject><subject>Advection</subject><subject>Constraints</subject><subject>fractional advection diffusion reaction equation</subject><subject>Galerkin method</subject><subject>Norms</subject><subject>Optimal control</subject><subject>optimal control problem</subject><subject>Optimization</subject><subject>Polynomials</subject><subject>spectral Galerkin method</subject><issn>0749-159X</issn><issn>1098-2426</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOwzAURS0EEqUw8AeWmBjS2o6T2COqoCAVGKASm-XEtkhJ49R2qLrxCXwjX4LbsDK9q6vzrt67AFxiNMEIkWnbryeEsCw9AiOMOEsIJfkxGKGC8gRn_O0UnHm_QgjjDPMR2L50ugpONnAuG-0-6haudXi3ChrroA8yaFjZ1kekbrWCtgv1OtLRC8420BponKxCbdvoSvWpD_rn61vVxvR-0E4PCNSbXu6FPwcnRjZeX_zNMVje3b7O7pPF8_xhdrNIKpIVaSIJLlVpcl4omilEc1MyZXhOpWKcFmlZlLykBU0zjFNJEK0yZjKlDVMVjhHpGFwNuZ2zm177IFa2d_FWL0jOGEspJnmkrgeqctZ7p43oXHzT7QRGYt-riL2KQ6-RnQ7stm707n9QPC0fh41fNEJ_AA</recordid><startdate>202209</startdate><enddate>202209</enddate><creator>Wang, Fangyuan</creator><creator>Zhou, Zhaojie</creator><general>John Wiley & Sons, Inc</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-0499-1545</orcidid></search><sort><creationdate>202209</creationdate><title>Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations</title><author>Wang, Fangyuan ; Zhou, Zhaojie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2573-a21bdbf697d45d046fb8df964ad89473b7b9b47435113a204c58f5def8dc1c253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>a priori error estimate</topic><topic>Advection</topic><topic>Constraints</topic><topic>fractional advection diffusion reaction equation</topic><topic>Galerkin method</topic><topic>Norms</topic><topic>Optimal control</topic><topic>optimal control problem</topic><topic>Optimization</topic><topic>Polynomials</topic><topic>spectral Galerkin method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Fangyuan</creatorcontrib><creatorcontrib>Zhou, Zhaojie</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>Aerospace 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>Numerical methods for partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Fangyuan</au><au>Zhou, Zhaojie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations</atitle><jtitle>Numerical methods for partial differential equations</jtitle><date>2022-09</date><risdate>2022</risdate><volume>38</volume><issue>5</issue><spage>1526</spage><epage>1542</epage><pages>1526-1542</pages><issn>0749-159X</issn><eissn>1098-2426</eissn><abstract>In this article a spectral Galerkin approximation of fractional advection diffusion optimal control problem with state constraint in L2 norm is discussed. The continuous first order optimality condition is derived. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for state, adjoint state, and control variables in Hα/2 and weighted L2 norms are derived. Numerical examples are presented to verify the theoretical findings.</abstract><cop>Hoboken, USA</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/num.22853</doi><tpages>33</tpages><orcidid>https://orcid.org/0000-0003-0499-1545</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0749-159X |
| ispartof | Numerical methods for partial differential equations, 2022-09, Vol.38 (5), p.1526-1542 |
| issn | 0749-159X 1098-2426 |
| language | eng |
| recordid | cdi_proquest_journals_2688834126 |
| source | Wiley Journals |
| subjects | a priori error estimate Advection Constraints fractional advection diffusion reaction equation Galerkin method Norms Optimal control optimal control problem Optimization Polynomials spectral Galerkin method |
| title | Spectral Galerkin method for state constrained optimal control of fractional advection‐diffusion‐reaction equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T07%3A47%3A40IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Spectral%20Galerkin%20method%20for%20state%20constrained%20optimal%20control%20of%20fractional%20advection%E2%80%90diffusion%E2%80%90reaction%20equations&rft.jtitle=Numerical%20methods%20for%20partial%20differential%20equations&rft.au=Wang,%20Fangyuan&rft.date=2022-09&rft.volume=38&rft.issue=5&rft.spage=1526&rft.epage=1542&rft.pages=1526-1542&rft.issn=0749-159X&rft.eissn=1098-2426&rft_id=info:doi/10.1002/num.22853&rft_dat=%3Cproquest_cross%3E2688834126%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2688834126&rft_id=info:pmid/&rfr_iscdi=true |