ADAPTIVE DISCONTINUOUS GALERKIN APPROXIMATION OF OPTIMAL CONTROL PROBLEMS GOVERNED BY TRANSIENT CONVECTION-DIFFUSION EQUATIONS

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YÜCEL H., Stoll M., Benner P.

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, cilt.48, ss.407-434, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1553/etna_vol48s407
  • Dergi Adı: ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.407-434
  • Anahtar Kelimeler: optimal control problem, a posteriori error estimate, discontinuous Galerkin method, convection diffusion equations, FINITE-ELEMENT-METHOD, CONSTRAINED OPTIMIZATION, ERROR ANALYSIS, A-PRIORI, VARIATIONAL DISCRETIZATION, SIPG METHOD, REGULARIZATION
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we investigate a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection diffusion equation. The control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method and by adding a Moreau-Yosida-type penalty function to the cost functional. Residual-based error estimators are proposed for both approaches. The derived error estimators are used as error indicators to guide the mesh refinements. A symmetric interior penalty Galerkin method in space and a backward Euler method in time are applied in order to discretize the optimization problem. Numerical results are presented, which illustrate the performance of the proposed error estimators.