Boundary Control Problems in Polyhedral Domains 

Project in the framework of the International Research Training Group (IGDK) 1754: Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures, financed by Deutschen Forschungsgemeinschaft (DFG) and the austrian Fond zur Förderung der wissenschaftlichen Forschung (FWF).


 Supervision: 


 Development: 

  • Max Winkler (UniBw München)
  • Sergejs Rogovs (UniBw München)


 Mentor: 

  • Johannes Pfefferer (UniBw München)


 Funding periods: 

  • 1. Funding period: March 2012 - August 2016
  • 2. Funding period: September 2016 - February 2021


 Goals: 

  • A priori error estimates for optimal boundary control
  • Local mesh refinement at corners and edges
  • Verification of the results with numerical tests


 PhD Theses: 

  • 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.


 Publications related to the project: 

  • 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, accepted by SIAM J. Numer. Anal. 2017 [Preprint]
  • Thomas Apel, Serge Nicaise, Johannes 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]