ADAPTIVE SYMMETRIC INTERIOR PENALTY GALERKIN METHOD FOR BOUNDARY CONTROL PROBLEMS


Creative Commons License

BENNER P., Yuecel H.

SIAM JOURNAL ON NUMERICAL ANALYSIS, vol.55, no.2, pp.1101-1133, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1137/15m1034507
  • Title of Journal : SIAM JOURNAL ON NUMERICAL ANALYSIS
  • Page Numbers: pp.1101-1133
  • Keywords: a posteriori error analysis, optimal boundary control problems, control constraints, adaptive finite element methods, discontinuous Galerkin methods, CONSTRAINED OPTIMAL-CONTROL, POSTERIORI ERROR ANALYSIS, CONVECTION-DIFFUSION EQUATIONS, PARTIAL-DIFFERENTIAL-EQUATIONS, FINITE-ELEMENT APPROXIMATION, 2ND-ORDER ELLIPTIC PROBLEMS, VARIATIONAL DISCRETIZATION, CONVERGENCE, STRATEGY

Abstract

We investigate an a posteriori error analysis of adaptive finite element approximations of linear-quadratic boundary optimal control problems under bilateral box constraints, which act on a Neumann boundary control. We use a symmetric interior Galerkin method as discretization technique. An efficient and reliable residual-type error estimator is introduced by invoking data oscillations. We then derive local upper and lower a posteriori error estimates for the boundary control problem. Adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical results are presented to illustrate the performance of the adaptive finite element approximation.