State Error Estimates for the Numerical Approximation of Sparse Distributed Control Problems in the Absence of Tikhonov Regularization

[1]  Eduardo Casas,et al.  UNIFORM CONVERGENCE OF THE FEM. APPLICATIONS TO STATE CONSTRAINED CONTROL PROBLEMS , 2002 .

[2]  R. Rannacher,et al.  Zur L∞-Konvergenz linearer finiter Elemente beim Dirichlet-Problem , 1976 .

[3]  Eduardo Casas,et al.  Critical Cones for Sufficient Second Order Conditions in PDE Constrained Optimization , 2019, SIAM J. Optim..

[4]  Michel Cristofol,et al.  Inverse Problem for a Curved Quantum Guide , 2012, Int. J. Math. Math. Sci..

[5]  Roland Herzog,et al.  Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with L1 Cost Functional , 2012, SIAM J. Optim..

[6]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[7]  Gerd Wachsmuth,et al.  Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems , 2017, SIAM J. Control. Optim..

[8]  Eduardo Casas,et al.  Second Order Analysis for Bang-Bang Control Problems of PDEs , 2012, SIAM J. Control. Optim..

[9]  Michael Hinze,et al.  A note on the approximation of elliptic control problems with bang-bang controls , 2010, Computational Optimization and Applications.

[10]  Boris Vexler,et al.  Finite element error analysis for state-constrained optimal control of the Stokes equations , 2008 .

[11]  Fredi Tröltzsch,et al.  Second Order and Stability Analysis for Optimal Sparse Control of the FitzHugh-Nagumo Equation , 2015, SIAM J. Control. Optim..

[12]  Daniel Wachsmuth,et al.  Stability for bang-bang control problems of partial differential equations , 2017, Optimization.

[13]  Alfred H. Schatz,et al.  Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates , 1998, Math. Comput..

[14]  Daniel Wachsmuth,et al.  Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations , 2017, 1705.01427.

[15]  Gerd Wachsmuth,et al.  Sufficient Second-Order Conditions for Bang-Bang Control Problems , 2017, SIAM J. Control. Optim..

[16]  Fredi Tröltzsch,et al.  First- and Second-Order Optimality Conditions for a Class of Optimal Control Problems with Quasilinear Elliptic Equations , 2009, SIAM J. Control. Optim..

[17]  Arnd Rösch,et al.  Error Estimates for Semilinear Parabolic Control Problems in the Absence of Tikhonov Term , 2019, SIAM J. Control. Optim..

[18]  Andrew R. Cameron Estimates For Solutions Of Elliptic Partial Differential Equations With Explicit Constants And Aspects Of The Finite Element Method For Second-Order Equations , 2010 .

[19]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[20]  Eduardo Casas Rentería A review on sparse solutions in optimal control of partial differential equations , 2017 .

[21]  C. Carstensen QUASI-INTERPOLATION AND A POSTERIORI ERROR ANALYSIS IN FINITE ELEMENT METHODS , 1999 .

[22]  Eduardo Casas,et al.  Optimal Control of Partial Differential Equations , 2017 .