OPTIMAL CONTROL OF THE LAPLACE-BELTRAMI OPERATOR ON COMPACT SURFACES： CONCEPT AND NUMERICAL TREATMENT
We consider optimal control problems of elliptic PDEs on hypersurfaces F in R^n for n = 2, 3. The leading part of the PDE is given by the Laplace-Beltrami operator, which is discretized by finite elements on a polyhedral approximation of F. The discrete optimal control problem is formulated on the a...
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| Veröffentlicht in: | Journal of computational mathematics 2012-07, Vol.30 (4), p.392-403 |
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| container_title | Journal of computational mathematics |
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| creator | Hinze, Michael Vierling, Morten |
| description | We consider optimal control problems of elliptic PDEs on hypersurfaces F in R^n for n = 2, 3. The leading part of the PDE is given by the Laplace-Beltrami operator, which is discretized by finite elements on a polyhedral approximation of F. The discrete optimal control problem is formulated on the approximating surface and is solved numerically with a semi-smooth Newton algorithm. We derive optimal a priori error estimates for problems including control constraints and provide numerical examples confirming our analytical findings. |
| doi_str_mv | 10.4208/jcm.1111-m3678 |
| format | Article |
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We derive optimal a priori error estimates for problems including control constraints and provide numerical examples confirming our analytical findings.</description><identifier>ISSN: 0254-9409</identifier><identifier>EISSN: 1991-7139</identifier><identifier>DOI: 10.4208/jcm.1111-m3678</identifier><language>eng</language><publisher>Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences</publisher><subject>Adjoints ; Approximation ; Equations of state ; Estimation methods ; Finite element method ; Hypersurfaces ; Iterative solutions ; Mathematical surfaces ; Newtons method ; Optimal control ; 半光滑牛顿算法 ; 数值处理 ; 数值求解 ; 最优控制问题 ; 有限元素 ; 椭圆偏微分方程 ; 紧凑型 ; 超曲面</subject><ispartof>Journal of computational mathematics, 2012-07, Vol.30 (4), p.392-403</ispartof><rights>Copyright 2012 AMSS, Chinese Academy of Sciences</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-57a43744d814e89efce9b8d5c7c6e37a809159dc6b0dd1f5ddc884919af17a9f3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/85761X/85761X.jpg</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/43693708$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/43693708$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,778,782,801,830,27907,27908,58000,58004,58233,58237</link.rule.ids></links><search><creatorcontrib>Hinze, Michael</creatorcontrib><creatorcontrib>Vierling, Morten</creatorcontrib><title>OPTIMAL CONTROL OF THE LAPLACE-BELTRAMI OPERATOR ON COMPACT SURFACES： CONCEPT AND NUMERICAL TREATMENT</title><title>Journal of computational mathematics</title><addtitle>Journal of Computational Mathematics</addtitle><description>We consider optimal control problems of elliptic PDEs on hypersurfaces F in R^n for n = 2, 3. 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We derive optimal a priori error estimates for problems including control constraints and provide numerical examples confirming our analytical findings.</description><subject>Adjoints</subject><subject>Approximation</subject><subject>Equations of state</subject><subject>Estimation methods</subject><subject>Finite element method</subject><subject>Hypersurfaces</subject><subject>Iterative solutions</subject><subject>Mathematical surfaces</subject><subject>Newtons method</subject><subject>Optimal control</subject><subject>半光滑牛顿算法</subject><subject>数值处理</subject><subject>数值求解</subject><subject>最优控制问题</subject><subject>有限元素</subject><subject>椭圆偏微分方程</subject><subject>紧凑型</subject><subject>超曲面</subject><issn>0254-9409</issn><issn>1991-7139</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNpNkDFOwzAYhS0EEqWwsiGZA7jYsRPbowkOrZTEUerOUeokpRVtIenCVTgLd-IKJLRC_Msb_u-94QPgluAJ87B42LjthPSHtjTg4gyMiJQEcULlORhhz2dIMiwvwVXXbTDG1GN8BFYms7NExTA0qc1NDE0E7VTDWGWxCjV61LHNVTKDJtO5siaHJu3ZJFOhhfNFHvXQ_Pvrc-iHOrNQpU8wXSQ6n4X9qs21solO7TW4aMrXrr455RgsIm3DKYrN80AiRz1-QD4vGeWMVYKwWsi6cbVcisp33AU15aXAkviycsESVxVp_KpyQjBJZNkQXsqGjsHkuOvafde1dVO8tett2X4UBBeDpqLXVAyail9NfeHuWNh0h337RzMaSMrx8L8_Db7sd6v39W71j_EYJRLTHxYfaaE</recordid><startdate>20120701</startdate><enddate>20120701</enddate><creator>Hinze, Michael</creator><creator>Vierling, Morten</creator><general>Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20120701</creationdate><title>OPTIMAL CONTROL OF THE LAPLACE-BELTRAMI OPERATOR ON COMPACT SURFACES： CONCEPT AND NUMERICAL TREATMENT</title><author>Hinze, Michael ; Vierling, Morten</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-57a43744d814e89efce9b8d5c7c6e37a809159dc6b0dd1f5ddc884919af17a9f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Adjoints</topic><topic>Approximation</topic><topic>Equations of state</topic><topic>Estimation methods</topic><topic>Finite element method</topic><topic>Hypersurfaces</topic><topic>Iterative solutions</topic><topic>Mathematical surfaces</topic><topic>Newtons method</topic><topic>Optimal control</topic><topic>半光滑牛顿算法</topic><topic>数值处理</topic><topic>数值求解</topic><topic>最优控制问题</topic><topic>有限元素</topic><topic>椭圆偏微分方程</topic><topic>紧凑型</topic><topic>超曲面</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hinze, Michael</creatorcontrib><creatorcontrib>Vierling, Morten</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><jtitle>Journal of computational mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hinze, Michael</au><au>Vierling, Morten</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>OPTIMAL CONTROL OF THE LAPLACE-BELTRAMI OPERATOR ON COMPACT SURFACES： CONCEPT AND NUMERICAL TREATMENT</atitle><jtitle>Journal of computational mathematics</jtitle><addtitle>Journal of Computational Mathematics</addtitle><date>2012-07-01</date><risdate>2012</risdate><volume>30</volume><issue>4</issue><spage>392</spage><epage>403</epage><pages>392-403</pages><issn>0254-9409</issn><eissn>1991-7139</eissn><abstract>We consider optimal control problems of elliptic PDEs on hypersurfaces F in R^n for n = 2, 3. 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| ispartof | Journal of computational mathematics, 2012-07, Vol.30 (4), p.392-403 |
| issn | 0254-9409 1991-7139 |
| language | eng |
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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy |
| subjects | Adjoints Approximation Equations of state Estimation methods Finite element method Hypersurfaces Iterative solutions Mathematical surfaces Newtons method Optimal control 半光滑牛顿算法 数值处理 数值求解 最优控制问题 有限元素 椭圆偏微分方程 紧凑型 超曲面 |
| title | OPTIMAL CONTROL OF THE LAPLACE-BELTRAMI OPERATOR ON COMPACT SURFACES： CONCEPT AND NUMERICAL TREATMENT |
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