Boundary concentrated finite elements for optimal control problems with distributed observation
We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a H 1 + δ ( Ω ) regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case th...
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| Veröffentlicht in: | Computational optimization and applications 2015-09, Vol.62 (1), p.31-65 |
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| container_title | Computational optimization and applications |
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| creator | Beuchler, S. Hofer, K. Wachsmuth, D. Wurst, J.-E. |
| description | We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a
H
1
+
δ
(
Ω
)
regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the
L
2
norm decreases like
N
-
δ
, where
N
is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of
Ω
. We present several numerical results. |
| doi_str_mv | 10.1007/s10589-015-9737-5 |
| format | Article |
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H
1
+
δ
(
Ω
)
regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the
L
2
norm decreases like
N
-
δ
, where
N
is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of
Ω
. We present several numerical results.</description><identifier>ISSN: 0926-6003</identifier><identifier>EISSN: 1573-2894</identifier><identifier>DOI: 10.1007/s10589-015-9737-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Approximation ; Boundary conditions ; Boundary element method ; Control theory ; Convex and Discrete Geometry ; Differential equations ; Discretization ; Estimates ; Finite element analysis ; Finite element method ; Management Science ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Norms ; Operations Research ; Operations Research/Decision Theory ; Optimization ; Partial differential equations ; Statistics ; Studies ; Texts ; Tracking</subject><ispartof>Computational optimization and applications, 2015-09, Vol.62 (1), p.31-65</ispartof><rights>Springer Science+Business Media New York 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-f769e53d4b23231ca04eb3ca719428d2a685f14a63626c6ef3fd1340548f6f3f3</citedby><cites>FETCH-LOGICAL-c349t-f769e53d4b23231ca04eb3ca719428d2a685f14a63626c6ef3fd1340548f6f3f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10589-015-9737-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10589-015-9737-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Beuchler, S.</creatorcontrib><creatorcontrib>Hofer, K.</creatorcontrib><creatorcontrib>Wachsmuth, D.</creatorcontrib><creatorcontrib>Wurst, J.-E.</creatorcontrib><title>Boundary concentrated finite elements for optimal control problems with distributed observation</title><title>Computational optimization and applications</title><addtitle>Comput Optim Appl</addtitle><description>We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a
H
1
+
δ
(
Ω
)
regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the
L
2
norm decreases like
N
-
δ
, where
N
is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of
Ω
. We present several numerical results.</description><subject>Approximation</subject><subject>Boundary conditions</subject><subject>Boundary element method</subject><subject>Control theory</subject><subject>Convex and Discrete Geometry</subject><subject>Differential equations</subject><subject>Discretization</subject><subject>Estimates</subject><subject>Finite element analysis</subject><subject>Finite element method</subject><subject>Management Science</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Norms</subject><subject>Operations Research</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Partial differential 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concentrated finite elements for optimal control problems with distributed observation</title><author>Beuchler, S. ; Hofer, K. ; Wachsmuth, D. ; Wurst, J.-E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c349t-f769e53d4b23231ca04eb3ca719428d2a685f14a63626c6ef3fd1340548f6f3f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Approximation</topic><topic>Boundary conditions</topic><topic>Boundary element method</topic><topic>Control theory</topic><topic>Convex and Discrete Geometry</topic><topic>Differential equations</topic><topic>Discretization</topic><topic>Estimates</topic><topic>Finite element analysis</topic><topic>Finite element method</topic><topic>Management Science</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Norms</topic><topic>Operations Research</topic><topic>Operations Research/Decision 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Appl</stitle><date>2015-09-01</date><risdate>2015</risdate><volume>62</volume><issue>1</issue><spage>31</spage><epage>65</epage><pages>31-65</pages><issn>0926-6003</issn><eissn>1573-2894</eissn><abstract>We consider the discretization of an optimal boundary control problem with distributed observation by the boundary concentrated finite element method. If the constraint is a
H
1
+
δ
(
Ω
)
regular elliptic PDE with smooth differential operator and source term, we prove for the two dimensional case that the discretization error in the
L
2
norm decreases like
N
-
δ
, where
N
is the number of unknowns. Our approach is suitable for solving a wide class of problems, among them piecewise defined data and tracking functionals acting only on a subdomain of
Ω
. We present several numerical results.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10589-015-9737-5</doi><tpages>35</tpages></addata></record> |
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| subjects | Approximation Boundary conditions Boundary element method Control theory Convex and Discrete Geometry Differential equations Discretization Estimates Finite element analysis Finite element method Management Science Mathematical analysis Mathematics Mathematics and Statistics Norms Operations Research Operations Research/Decision Theory Optimization Partial differential equations Statistics Studies Texts Tracking |
| title | Boundary concentrated finite elements for optimal control problems with distributed observation |
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