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Projekt Diskretisierung von Optimalsteuerproblemen

DFG-Projekt: Numerical analysis and discretization strategies for optimal control problems with singularities

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DFG-Schwerpunktprogramm 1253: Optimization with PDE constraints

LEITUNG:

BEARBEITER:

KOOPERATIONSPARTNER:

Förderungszeiträume

  • 2. Förderungszeitraum: Seit Oktober 2009
  • 1. Förderungszeitraum: Oktober 2006 - September 2009
    Dies ist ein gemeinsames Projekt von DFG und FWF. Der FWF-Anteil des Projekts ist in Projekt P18971-N18 organisiert.

ZIELE:

  • A priori Fehlerabschätzungen für Optimalsteuerprobleme mit Kontrollbeschränkungen
  • A priori Fehlerabschätzungen bei punktweisen Zustandsbeschränkungen
  • A posteriori Fehlerschätzer bei Kontrollbeschränkungen
  • A posteriori Fehlerschätzer bei Zustandsbeschränkungen
  • Verifizierung aller Untersuchungen durch entsprechende numerische Tests

VERÖFFENTLICHUNGEN AUS DEM PROJEKT:

  • Thomas Apel, Johannes Pfefferer, Arnd Rösch: Finite element error estimates for Neumann boundary control problems on graded meshes. Comput. Optim. Appl., published online, 2011 [DOI: 10.1007/s10589-011-9427-x | Preprint SPP1253-087]
  • Apel, T., Flaig, T. G., Crank-Nicolson Schemes for Optimal Control Problems with Evolution Equations, submitted, 2010. [preprint: pdf-file]
  • Rösch, A., Steinig, S., A Priori Error Estimates for a State-Constrained Elliptic Optimal Control Problem, Preprint SPP1253-111, DFG Priority Program 1253, Erlangen, 2010.
  • Rösch, A., Wachsmuth, D., A-Posteriori Error Estimates for Optimal Control Problems with State and Control Constraints, Preprint SPP1253-110, DFG Priority Program 1253, Erlangen, 2010.
  • Krumbiegel, K., Neitzel, I., Rösch, A., Sufficient optimality conditions for the Moreau-Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints, Mathematics and its Applications / Annals of AOSR, 2(2): 222-246, 2010.
  • Krumbiegel, K., Neitzel, I., Rösch, A., Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints, Computational Optimization and Applications, published electronically, 2010.
  • Krumbiegel, K., Meyer, C., Rösch, A., A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints, SIAM Journal Control and Optimization 48(8): 5108-5142, 2010.
  • Sirch, D., Finite Element Error Analysis for PDE-constrained Optimal Control Problems: The Control Constrained Case Under Reduced Regularity, PhD thesis, TU München, 2010. [pdf-file]
  • Apel, T., Sirch, D., A priori mesh grading for distributed optimal control problems, accepted for: G. Leugering et al. (eds.): Themenband SPP 1253 (Arbeitstitel), 2010. [preprint: pdf-file]
  • Cherednichenko, S., Rösch, A., Error Estimates for the Discretization of Elliptic Control Problems with Pointwise Control and State Constraints, Computational Optimization and Applications 44(1):27-55, 2009.
  • Apel, T., Benedix, O., Sirch, D., Vexler, B., A priori mesh grading for an elliptic problem with Dirac right-hand side, submitted, 2009. [preprint: pdf-file]
  • Nicaise, S., Sirch, D., Optimal control of the Stokes equations: Conforming and non-conforming finite element methods under reduced regularity, Comput. Optim. Appl., 2009 [ DOI:10.1007/s10589-009-9305-y | Preprint ]
  • Winkler, G., Control constrained optimal control problems in non-convex three dimensional polyhedral domains, PhD thesis, TU Chemnitz, 2008. [pdf-file]
  • Apel, T., Sirch, D., Winkler, G., Error estimates for control constrained optimal control problems: Discretization with anisotropic finite element meshes, Preprint SPP1253-02-06, DFG Priority Program 1253, Erlangen, 2008. Submitted to Math. Program.
  • May, S., Rannacher, R., Vexler, B., Error analysis for a finite element approximation of elliptic Dirichlet boundary control problems, submitted, 2008. [pdf-file]
  • Kröner, A., Vexler, B., A priori error estimates for elliptic optimal control problems with bilinear state equation, submitted, 2008. [pdf-file]
  • de los Reyes, J. C., Meyer, C., Vexler,B., Finite element error analysis for state-constrained optimal control of the Stokes equations, Control and Cybernetics, to appear, 2008. [pdf-file]
  • Apel, T., Rösch, A., Sirch, D., L∞-error estimates on graded meshes with application to optimal control, SIAM J. Control Optim. 48(2009), 1771-1796. [ DOI 10.1137/080731724 | Preprint ]
  • Merino, P., Tröltzsch, F., Vexler, B., Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44(1), 167-188, 2010. [preprint: pdf-file]
  • Apel, T., Sirch, D., L2-error estimates for the Dirichlet and Neumann problem on anisotropic finite element meshes, Preprint SPP1253-02-05 , DFG Priority Program 1253, Erlangen, 2008. Accepted for publication in Appl. Math.
  • Benedix, O., Vexler, B., A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints, Computational Optimization and Applications 44(1), 3-25, 2009. [preprint: pdf-file]
  • Apel, T., Rösch, A., Winkler, G., Optimal control in nonconvex domains: a priori discretization error estimates, Calcolo 44(2007), 137-158. [preprint: ps-file pdf-file]
  • Apel, T., Winkler, G., Optimal Control Under Reduced Regularity. Appl. Numer. Math., 59(2009), 2050-2064. [DOI 10.1016/j.apnum.2008.12.003 | Preprint ]
  • Vexler, B., Wollner, W., Adaptive finite elements for elliptic optimization problems with control constraints, SPP 1253-Preprint Nr.: SPP1253-23-01, accepted for publication in: SIAM Journal on Control and Optimization, 2007. [preprint: pdf-file ]
  • Meidner, D., Vexler, B., A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems. Part I: Problems without Control Constraints, SIAM Journal on Control and Optimization, 47(3):1150-1177, 2008.[ pdf-file ]
  • Meidner, D., Vexler, B., A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems. Part II: Problems with Control Constraints, SIAM Journal on Control and Optimization, 47(3):1301-1329, 2008.[ pdf-file ]
  • Rösch, A., Vexler, B., Optimal control of the Stokes equations: A priori error analysis for finite element discretization with postprocessing, SIAM Journal Numerical Analysis, 44(5):1903-1920, 2006 [pdf-file]
  • Apel, T., Rösch, A., Winkler, G., Discretization error estimates for an optimal control problem in a nonconvex domain, in: A. Bermúdez de Castro et al. (eds.): Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005, 299--307, Springer, Berlin, 2006