Convergence of discontinuous galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

Chrysafinos, K

dc.contributor.author	Chrysafinos, K	en
dc.date.accessioned	2014-03-01T01:33:04Z
dc.date.available	2014-03-01T01:33:04Z
dc.date.issued	2010	en
dc.identifier.issn	0764-583X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20302
dc.subject	Discontinuous Galerkin approximations	en
dc.subject	Distributed controls	en
dc.subject	Semi-linear parabolic PDE's	en
dc.subject	Stability estimates	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	BOUNDARY CONTROL-PROBLEMS	en
dc.subject.other	FINITE-ELEMENT METHODS	en
dc.subject.other	CONTROL CONSTRAINTS	en
dc.subject.other	EQUATIONS	en
dc.subject.other	DISCRETIZATION	en
dc.title	Convergence of discontinuous galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's	en
heal.type	journalArticle	en
heal.identifier.primary	10.1051/m2an/2009046	en
heal.identifier.secondary	http://dx.doi.org/10.1051/m2an/2009046	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE's is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions of the continuous optimality system is shown. The proof is based on stability estimates at arbitrary time points under minimal regularity assumptions, and a discrete compactness argument for discontinuous Galerkin schemes (see Walkington [SINUM (June 2008) (submitted), preprint available at http://www.math.cmu.edu/̃noelw], Sects. 3, 4). © EDP Sciences, SMAI 2009.	en
heal.publisher	EDP SCIENCES S A	en
heal.journalName	ESAIM: Mathematical Modelling and Numerical Analysis	en
dc.identifier.doi	10.1051/m2an/2009046	en
dc.identifier.isi	ISI:000275318800007	en
dc.identifier.volume	44	en
dc.identifier.issue	1	en
dc.identifier.spage	189	en
dc.identifier.epage	206	en