Boundary Control Problems in Polyhedral Domains 

ein Projekt im Graduiertenkolleg International Research Training Group (IGDK) 1754: Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures

Das Graduiertenkolleg wird gemeinsam von der Deutschen Forschungsgemeinschaft (DFG) und dem österreichischen Fonds zur Förderung der wissenschaftlichen Forschung (FWF) finanziert.


 Leitung: 

  • Thomas Apel
  • Olaf Steinbach
  • Boris Vexler


 Bearbeiter: 

  • Max Winkler
  • Sergejs Rogovs
  • Christof Haubner


 Mentor: 

  • Johannes Pfefferer


 Förderungszeiträume: 

  • 1. Förderungszeitraum: März 2012 - August 2016
  • 2. Förderungszeitraum: September 2016 - Februar 2021


 Ziele: 

  • A priori Fehlerabschätzungen für optimale Randsteuerprobleme
  • Lokale Netzverfeinerung an Ecken und Kanten
  • Verifizierung der Untersuchungen durch entsprechende numerische Tests


 Abschlussarbeiten aus dem Projekt: 

  • Pfefferer, J.: Numerical analysis for elliptic Neumann boundary control problems on polygonal domains, PhD Thesis, UniBw München, 2014. [Dissertation]
  • Winkler, M.: Finite element error analysis for Neumann boundary control problems on polygonal and polyhedral domains, PhD Thesis, UniBw München, 2015. [Dissertation]
  • Sergejs Rogovs: Pointwise Error Estimates for Boundary Control Problems on Polygonal Domains,  PhD Thesis, UniBw München, 2018. [Dissertation]


 Veröffentlichungen aus dem Projekt: 

  • Thomas Apel, Johannes Pfefferer, Sergejs Rogovs, Max Winkler: L∞-error estimates for Neumann boundary value problems on graded meshes. Accepted by IMA J. Numer. Anal. [Preprint]
  • Thomas Apel, Johannes Pfefferer, Max Winkler: Error estimates for the postprocessing approach applied to Neumann boundary control problems in polyhedral domains. IMA J. Numer. Anal. 38(2018)4,  1984–2025. [Paper] / [Preprint]
  • Thomas Apel, Serge Nicaise, Johannes Pfefferer: Adapted numerical methods for the numerical solution of the Poisson equation with L2 boundary data in non-convex domains. SIAM J. Numer. Anal. 55(2017), 1937-1957 [Paper] / [Preprint]
  • Thomas Apel, Serge Nicaise, Johann[es Pfefferer: Discretization of the Poisson equation with non-smooth boundary data and emphasis on non-convex domains, Numer. Methods PDE, 32(2016), 1433–1454. [Paper] / [Preprint]
  • Thomas Apel, Mariano Mateos, Johannes Pfefferer, Arnd Rösch: On the regularity of the solutions of Dirichlet optimal control problems in polygonal domains, SIAM J. Control Optim. 53(2015), 3620–3641. [Paper] / [Preprint]
  • Neitzel, I., Pfefferer, J., Rösch, A.: Finite element discretization of state-constrained elliptic optimal control problems with semilinear state equation, SIAM J. Control. Optim, 53(2):974-904, 2015. [Paper] / [Preprint]
  • Apel, T., Pfefferer, J., Rösch, A.: Finite element error estimates on the boundary with application to optimal control, Math. Comp. 84(291): 33-70, 2015. [Paper] / [Preprint]
  • Apel, T., Lombardi, A. L., Winkler, M.: Anisotropic mesh refinement in polyhedral domains: error estimates with data in L^2(Ω), ESAIM. Math. Model. Numer. Anal. 48(4): 1117-1145, 2014. [Paper] / [Preprint]
  • Apel, T., Pfefferer, J., Winkler, M.: Local Mesh Refinement for the Discretization of Neumann Boundary Control Problems on Polyhedra, Math. Methods Appl. Sci., 39(5):1206-1232, 2016. [Paper] / [Preprint]
  • Apel, T., Steinbach, O., Winkler, M.: Error Estimates for Neumann Boundary Control Problems with Energy Regularization, J. Numer. Math 24(4):207-233, 2016. [Paper]
  • Klaus Krumbiegel, Johannes Pfefferer: Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations, Comput. Optim. Appl., 61(2):373-408, 2015. [Paper] / [Preprint]
  • Grossmann, C., Winkler, M.: Mesh-Independent Convergence of Penalty Methods Applied to Optimal Control with Partial Differential Equations, Optimization 62(5): 629-647, 2013. [Paper]
  • Grossmann, C., Winkler, M.: A Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control, Schedae Informaticae 21: 9-26, 2012. [Paper]