Mass Lumping for the Optimal Control of Elliptic Partial Differential Equations
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[1] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.
[2] G. Fix. Review: Philippe G. Ciarlet, The finite element method for elliptic problems , 1979 .
[3] Andreas Springer,et al. Third order convergent time discretization for parabolic optimal control problems with control constraints , 2013, Computational Optimization and Applications.
[4] René Schneider,et al. A Posteriori Error Estimation for Control-Constrained, Linear-Quadratic Optimal Control Problems , 2016, SIAM J. Numer. Anal..
[5] Winfried Sickel,et al. Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations , 1996, de Gruyter series in nonlinear analysis and applications.
[6] Konstantin Pieper,et al. Finite element discretization and efficient numerical solution of elliptic and parabolic sparse control problems , 2015 .
[7] Eduardo Casas,et al. Error estimates for the numerical approximation of Neumann control problems , 2008, Comput. Optim. Appl..
[8] Arnd Rösch,et al. Error estimates for linear-quadratic control problems with control constraints , 2006, Optim. Methods Softw..
[9] René Schneider,et al. Achieving optimal convergence order for FEM in control constrained optimal control problems , 2015 .
[10] Anders Logg,et al. Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book , 2012 .
[11] Michael Hinze,et al. A note on the approximation of elliptic control problems with bang-bang controls , 2010, Computational Optimization and Applications.
[12] Gerd Wachsmuth,et al. Convergence and regularization results for optimal control problems with sparsity functional , 2011 .
[13] T. Geveci,et al. On the approximation of the solution of an optimal control problem governed by an elliptic equation , 1979 .
[14] Thomas Apel. Interpolation in h‐Version Finite Element Spaces , 2004 .
[15] L. R. Scott,et al. The Mathematical Theory of Finite Element Methods , 1994 .
[16] Michael Hinze,et al. A Variational Discretization Concept in Control Constrained Optimization: The Linear-Quadratic Case , 2005, Comput. Optim. Appl..
[17] Jean E. Roberts,et al. Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation , 2000, SIAM J. Numer. Anal..
[18] T. Apel. Anisotropic Finite Elements: Local Estimates and Applications , 1999 .
[19] Roland Herzog,et al. Approximation of sparse controls in semilinear equations by piecewise linear functions , 2012, Numerische Mathematik.
[20] M. Rivara,et al. Local modification of meshes for adaptive and/or multigrid finite-element methods , 1991 .
[21] Djalil Kateb,et al. On the boundedness of the mapping f ↦ |f|μ, μ > 1 on Besov spaces , 2003 .
[22] Richard S. Falk,et al. Approximation of a class of optimal control problems with order of convergence estimates , 1973 .
[23] Arnd Rösch,et al. Finite element error estimates for Neumann boundary control problems on graded meshes , 2011, Computational Optimization and Applications.
[24] Anders Logg,et al. The FEniCS Project Version 1.5 , 2015 .
[25] Arnd Rösch,et al. Superconvergence Properties of Optimal Control Problems , 2004, SIAM J. Control. Optim..
[26] David Sevilla,et al. Polynomial integration on regions defined by a triangle and a conic , 2010, ISSAC.
[27] Y. Meyer,et al. Fonctions qui opèrent sur les espaces de Sobolev , 1991 .
[28] Arnd Rösch,et al. Error estimates for finite element approximations of elliptic control problems , 2007 .