Open Access
| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 3159 - 3204 | |
| DOI | https://doi.org/10.1051/m2an/2025086 | |
| Published online | 01 December 2025 | |
- G. Alberti, S. Bianchini and G. Crippa, Structure of level sets and Sard-type properties of Lipschitz maps. Ann. Sc. Norm. Super. Pisa Cl. Sci. XII (2013) 863–902. [Google Scholar]
- N. Arada, E. Casas and F. Tröltzsch, Error estimates for the numerical approximation of a semilinear elliptic control problem. Comput. Optim. Appl. 23 (2002) 201–229. [CrossRef] [MathSciNet] [Google Scholar]
- T. Bayen, J.F. Bonnans and F.J. Silva, Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations. Trans. Amer. Math. Soc. 366 (2014) 2063–2087. [Google Scholar]
- A. Behzadan and M. Holst, Multiplication in Sobolev spaces, revisited. Ark. Mat. 59 (2021) 275–306. [Google Scholar]
- A. Bejan, Convection Heat Transfer, 4 edition. J. Wiley & Sons (2013). [Google Scholar]
- J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer-Verlag, Berlin, Heidelberg (2000). [Google Scholar]
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics. Springer-Verlag, New York (2008). [Google Scholar]
- C. Carstensen, Quasi-interpolation and a posteriori error analysis in finite element methods. ESAIM: Math. Modell. Numer. Anal. 33 (1999) 1187–1202. [Google Scholar]
- E. Casas and V. Dhamo, Error estimates for the numerical approximation of a quasilinear Neumann problem under minimal regularity of the data. Numer. Math. 117 (2011) 115–145. [Google Scholar]
- E. Casas and V. Dhamo, Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations. Comput. Optim. Appl. 52 (2012) 719–756. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas and M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems. Comput. Appl. Math. 21 (2002) 67–100. [MathSciNet] [Google Scholar]
- E. Casas and F. Tröltzsch, First- and second-order optimality conditions for a class of optimal control problems with quasilinear elliptic equations. SIAM J. Control Optim. 48 (2009) 688–718. [Google Scholar]
- E. Casas and F. Tröltzsch, Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations. ESAIM:COCV 17 (2011) 771–800. [CrossRef] [EDP Sciences] [Google Scholar]
- E. Casas and F. Tröltzsch, A general theorem on error estimates with application to a quasilinear elliptic optimal control problem. Comput. Optim. Appl. 53 (2012) 173–206. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, M. Mateos and F. Tröltzsch, Error estimates for the numerical approximation of boundary semilinear elliptic control problems. Comput. Optim. Appl. 31 (2005) 193–219. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, M. Mateos and J.-P. Raymond, Error estimates for the numerical approximation of a distributed control problem for the steady-state Navier–Stokes equations. SIAM J. Control Optim. 46 (2007) 952–982. [CrossRef] [MathSciNet] [Google Scholar]
- E. Casas, M. Mateos and A. Rösch, Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations. Numer. Math. 149 (2021) 305–340. [CrossRef] [MathSciNet] [Google Scholar]
- M. Chipot, Elliptic Equations: An Introductory Course. Birkh¨auser Verlag, Basel (2009). [Google Scholar]
- C. Christof and C. Meyer, A note on a priori Lp-error estimates for the obstacle problem. Numer. Math. 139 (2018) 27–45. [Google Scholar]
- P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Classics in Applied Mathematics. SIAM (2002). [Google Scholar]
- S. Clain, Elliptic operators of divergence type with Hölder coefficients in fractional Sobolev spaces. Rend. Mat. Appl. 17 (1997) 207–236. [Google Scholar]
- C. Clason, V.H. Nhu and A. Rösch, No-gap second-order optimality conditions for optimal control of a non-smooth quasilinear elliptic equation. ESAIM: COCV 27 (2021) 62. [CrossRef] [EDP Sciences] [Google Scholar]
- C. Clason, V.H. Nhu and A. Rösch, Optimal control of a non-smooth quasilinear elliptic equation. Math. Control Related Fields 11 (2021) 521–554. [Google Scholar]
- C. Clason, V.H. Nhu and A. Rösch, Numerical analysis of a nonsmooth quasilinear elliptic control problem: I. Explicit second-order optimality conditions. ESAIM: Math. Modell. Numer. Anal. (ESAIM: M2AN) 58 (2024) 993–1029. [Google Scholar]
- B. Dacorogna, Direct Methods in the Calculus of Variations. Applied Mathematical Sciences, 2 edition. Springer (2008). [Google Scholar]
- J.C. De Los Reyes and V. Dhamo, Error estimates for optimal control problems of a class of quasilinear equations arising in variable viscosity fluid flow. Numer. Math. 132 (2016) 691–720. [Google Scholar]
- J.C. De Los Reyes, C. Meyer and B. Vexler, Finite element error analysis for state-constrained optimal control of the Stokes equations. Control Cybern. 37 (2008) 251–284. [Google Scholar]
- K. Deckelnick and M. Hinze, Convergence of a finite element approximation to a state-constrained elliptic control problem. SIAM J. Numer. Anal. 45 (2007) 1937–1953. [Google Scholar]
- T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces. Math. Comput. 34 (1980) 441–463. [Google Scholar]
- L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Function, 4th edition. CRC Press, New York (1992). [Google Scholar]
- R.S. Falk, Approximation of a class of optimal control problems with order of convergence estimates. J. Math. Anal. Appl. 44 (1973) 28–47. [Google Scholar]
- T. Geveci, On the approximation of the solution of an optimal control problem governed by an elliptic equation. RAIRO. Anal. Numér. 13 (1979) 313–328. [Google Scholar]
- D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, Heidelberg (2001). [Google Scholar]
- P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Advanced Pub. Program (1985). [Google Scholar]
- M. Hinze, A variational discretization concept in control constrained optimization: the linear-quadratic case. Comput. Optim. Appl. 30 (2005) 45–61. [Google Scholar]
- M. Hinze and F. Tröltzsch, Discrete concepts versus error analysis in PDE-constrained optimization. GAMM-Mitteilungen 33 (2010) 148–162. [Google Scholar]
- M. Holtmannspötter and A. Rösch, A priori error estimates for the finite element approximation of a nonsmooth optimal control problem governed by a coupled semilinear PDE-ODE system. SIAM J. Control Optim. 59 (2021) 3329–3358. [Google Scholar]
- K. Ito and K. Kunisch, Lagrange Multiplier Approach to Variational Problems and Applications. Advances in Design and Control. SIAM (2008). [Google Scholar]
- A. Kufner, O. John and S. Fučík, Function Spaces. Noordhoff International Publishing, Leyden; Academia, Prague (1977). Monographs and Textbooks on Mechanics of Solids and Fluids; Mechanics: Analysis. [Google Scholar]
- C. Meyer and A. Rösch, Superconvergence properties of optimal control problems. SIAM J. Control Optim. 43 (2004) 970–985. [Google Scholar]
- C. Meyer and A. Rösch, L∞-estimates for approximated optimal control problems. SIAM J. Control Optim. 44 (2005) 1636–1649. [Google Scholar]
- C. Meyer and O. Thoma, A priori finite element error analysis for optimal control of the obstacle problem. SIAM J. Numer. Anal. 51 (2013) 605–628. [Google Scholar]
- I. Neitzel, J. Pfefferer and A. Rösch, Finite element discretization of state-constrained elliptic optimal control problems with semilinear state equation. SIAM J. Control Optim. 53 (2015) 874–904. [Google Scholar]
- G. Savaré, Regularity results for elliptic equations in Lipschitz domains. J. Funct. Anal. 152 (1998) 176–201. [CrossRef] [MathSciNet] [Google Scholar]
- M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces. MOS-SIAM Series on Optimization. SIAM (2011). [Google Scholar]
- Y.B. Zel’dovich and Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Academic Press (1966). [Google Scholar]
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