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All issues Volume 59 / No 2 (March-April 2025) ESAIM: M2AN, 59 2 (2025) 749-787 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
Page(s) 749 - 787
DOI https://doi.org/10.1051/m2an/2025006
Published online 24 March 2025
  1. T. Apel, M. Mateos, J. Pfefferer and A. Rösch, On the regularity of the solutions of Dirichlet optimal control problems in polygonal domains. SIAM J. Control Optim. 53 (2015) 3620–3641. [Google Scholar]
  2. T. Apel, M. Mateos, J. Pfefferer and A. Rösch, Error estimates for Dirichlet control problems in polygonal domains: quasi-uniform meshes. Math. Control Related Fields 8 (2018) 217–245. [Google Scholar]
  3. N. Arada and J.P. Raymond, Dirichlet boundary control of semilinear parabolic equations. Part 1: problems with no state constraints. Appl. Math. Optim. 45 (2002) 125–143. [MathSciNet] [Google Scholar]
  4. F.B. Belgacem, C. Bernardi and H.E. Fekih, Dirichlet boundary control for a parabolic equation with a final observation I: a space-time mixed formulation and penalization. Asymptot. Anal. 71 (2011) 101–121. [MathSciNet] [Google Scholar]
  5. M. Berggren, Approximation of very weak solutions to boundary value problems. SIAM J. Numer. Anal. 42 (2004) 860–877. [Google Scholar]
  6. K. Bhandari, J. Lemoine and A. Münch, Global boundary null-controllability of one-dimensional semilinear heat equations. Discrete Contin. Dyn. Syst. Ser. S 17 (2024) 2251–2297. [Google Scholar]
  7. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3rd edition. Springer, New York (2008). [Google Scholar]
  8. E. Casas and K. Chrysafinos, A discontinuous Galerkin time-stepping scheme for the velocity tracking problem. SIAM J. Numer. Anal. 50 (2012) 2281–2306. [Google Scholar]
  9. E. Casas and J.P. Raymond, Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations. SIAM J. Control Optim. 45 (2006) 1586–1611. [Google Scholar]
  10. E. Casas and J. Sokolowski, Approximation of boundary control problems on curved domains. SIAM J. Control Optim. 48 (2010) 3746–3780. [Google Scholar]
  11. E. Casas, M. Mateos and J.P. Raymond, Penalization of Dirichlet optimal control problems. ESAIM Control Optim. Calc. Var. 15 (2009) 782–809. [Google Scholar]
  12. K. Chrysafinos, Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDEs. ESAIM: Math. Model. Numer. Anal. 44 (2010) 189–206. [Google Scholar]
  13. P.G. Ciarlet, The Finite Element Methods for Elliptic Problems, 1st edition. Vol. 4. North-Holland (1978). [Google Scholar]
  14. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numer. 9 (1975) 77–84. [Google Scholar]
  15. K. Deckelnick, A. Günther and M. Hinze, Finite element approximation of Dirichlet boundary control for elliptic PDEs on two and three-dimensional curved domains. SIAM J. Control Optim. 48 (2009) 2798–2819. [Google Scholar]
  16. L.C. Evans, Partial Differential Equations, 2nd edition. Vol. 19. AMS (2002). [Google Scholar]
  17. D.A. French and J.T. King, Analysis of a robust finite element approximation for a parabolic equation with rough boundary data. Math. Comput. 60 (1993) 79–104. [Google Scholar]
  18. D.A. French and J.T. King, Approximation of an elliptic control problem by the finite element method. Numer. Funct. Anal. Optim. 12 (1991) 299–314. [Google Scholar]
  19. A.V. Fursikov, M.D. Gunzburger and L.S. Hou, Boundary value problems and optimal boundary control for the Navier–Stokes systems: the two-dimensional case. SIAM J. Control Optim. 36 (1998) 852–894. [CrossRef] [MathSciNet] [Google Scholar]
  20. V. Girault and P.A. Raviart, Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms. Springer (1986). [Google Scholar]
  21. W. Gong and B.Y. Li, Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems. IMA J. Numer. Anal. 40 (2020) 2898–2939. [CrossRef] [MathSciNet] [Google Scholar]
  22. W. Gong, M. Hinze and Z.J. Zhou, A priori error analysis for finite element approximation of parabolic optimal control problems with pointwise control. SIAM J. Control Optim. 52 (2014) 97–119. [CrossRef] [MathSciNet] [Google Scholar]
  23. W. Gong, M. Hinze and Z.J. Zhou, Finite element method and a priori error estimates for Dirichlet boundary control problems governed by parabolic PDEs. J. Sci. Comput. 66 (2016) 941–967. [MathSciNet] [Google Scholar]
  24. M.D. Gunzburger, L.S. Hou and T.P. Svobodny, Analysis and finite element approximation of optimal control problems for the stationary Navier–Stokes equations with Dirichlet controls. RAIRO Modél. Math. Anal. Numér. 25 (1991) 711–748. [MathSciNet] [Google Scholar]
  25. M. Hinze, A variational discretization concept in control constrained optimization: the linear-quadratic case. Comput. Optim. Appl. 30 (2005) 45–61. [Google Scholar]
  26. M. Hinze and K. Kunisch, Second order methods for boundary control of the instationary Navier–Stokes system. Z. Angew. Math. Mech. 84 (2004) 171–187. [Google Scholar]
  27. M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich, Optimization with PDE Constraints. Vol. 23. Springer-Netherlands (2009). [Google Scholar]
  28. A. Kufner, L. Persson and N. Samko, Weighted Inequalities of Hardy Type, 2nd edition. World Scientific Publishing Company (2017). [Google Scholar]
  29. K. Kunisch and B. Vexler, Constrained Dirichlet boundary control in L2 for a class of evolution equations. SIAM J. Control Optim. 46 (2007) 1726–1753. [Google Scholar]
  30. I. Lasiecka, Unified theory for abstract parabolic boundary problems – a semigroup approach. Appl. Math. Optim. 6 (1980) 287–333. [MathSciNet] [Google Scholar]
  31. I. Lasiecka, Galerkin approximations of abstract parabolic boundary value problems with rough boundary data – Lp theory. Math. Comput. 47 (1986) 55–75. [Google Scholar]
  32. I. Lasiecka and K. Malanowski, On discrete-time Ritz-Galerkin approximation of control constrained optimal control problems for parabolic systems. Control Cybern. 7 (1978) 21–36. [Google Scholar]
  33. B.J. Li, H. Luo and X.P. Xie, Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data. Fract. Calc. Appl. Anal. 25 (2022) 747–782. [CrossRef] [MathSciNet] [Google Scholar]
  34. J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, 1st edition. Vol. 170. Springer, Berlin (1971). [Google Scholar]
  35. J.L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problem and Applications. Vol. 1. Springer, New York (1972). [Google Scholar]
  36. J.L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problem and Applications. Vol. 2. Springer, New York (1972). [Google Scholar]
  37. S. May, R. Rannacher and B. Vexler, Error analysis fo a finite element approximation of elliptic Dirichlet boundary control problems. SIAM J. Control Optim. 51 (2013) 2585–2611. [Google Scholar]
  38. D. Meidner and B. Vexler, A priori error estimates for space-time finite element discretization of parabolic optimal control problems. I: Problems without control constraints. SIAM J. Control Optim. 47 (2008) 1150–1177. [Google Scholar]
  39. D. Meidner and B. Vexler, A priori error estimates for space-time finite element discretization of parabolic optimal control problems. II. Problems with control constraints. SIAM J. Control Optim. 47 (2008) 1301–1329. [CrossRef] [MathSciNet] [Google Scholar]
  40. G. Of, T.X. Phan and O. Steinbach, An energy space finite element approach for elliptic Dirichlet boundary control problems. Numer. Math. 129 (2015) 723–748. [Google Scholar]
  41. D. Schötzau, Hp-DGFEM for Parabolic Evolution Problems. Ph.D thesis, Swiss Federal Institute of Technology, Zürich (1999). [Google Scholar]
  42. J. Sokolowski and J.P. Zolesio, Introduction to Shape Optimization: Shape Sensitivity Analysis, 1st edition. Springer-Verlag, Berlin (1992). [Google Scholar]
  43. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, 2nd edition. Springer-Verlag, Berlin (1997). [Google Scholar]
  44. F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications. Vol. 12. AMS, Providence, Rhode Island (2010). [Google Scholar]
  45. N. von Daniels, M. Hinze and M. Vierling, Crank–Nicolson time stepping and variational discretization of control-constrained parabolic optimal control problems. SIAM J. Control Optim. 53 (2015) 1182–1198. [CrossRef] [MathSciNet] [Google Scholar]

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