Error estimates in $ L^2 $ and $ L^\infty $ norms of finite volume method for the bilinear elliptic optimal control problem

[1]  W. Gibbs,et al.  Finite element methods , 2017, Graduate Studies in Mathematics.

[2]  Aihui Zhou,et al.  A Note on the Optimal L2-Estimate of the Finite Volume Element Method , 2002, Adv. Comput. Math..

[3]  Danping Yang,et al.  A PRIORI ERROR ESTIMATE AND SUPERCONVERGENCE ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF BILINEAR TYPE , 2008 .

[4]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[5]  Ruo Li,et al.  Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems , 2002, SIAM J. Control. Optim..

[6]  Haiying Wang,et al.  Journal of Computational and Applied Mathematics a Posteriori Error Analysis of a Cell-centered Finite Volume Method for Semilinear Elliptic Problems , 2022 .

[7]  Yanping Chen,et al.  Error estimates for parabolic optimal control problem by fully discrete mixed finite element methods , 2010 .

[8]  Zhiqiang Cai,et al.  On the finite volume element method , 1990 .

[9]  Ningning Yan,et al.  A posteriori error estimates for control problems governed by nonlinear elliptic equations , 2003 .

[10]  Ulrich Langer,et al.  Unstructured space-time finite element methods for optimal control of parabolic equations , 2020, SIAM J. Sci. Comput..

[11]  Fenglin Huang,et al.  A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Stokes Equations , 2011, SIAM J. Numer. Anal..

[12]  Qian Li,et al.  Error estimates in L2, H1 and Linfinity in covolume methods for elliptic and parabolic problems: A unified approach , 1999, Math. Comput..

[13]  D. Rose,et al.  Some errors estimates for the box method , 1987 .

[14]  Tao Lin,et al.  On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials , 2001, SIAM J. Numer. Anal..

[15]  Yanping Chen,et al.  A Posteriori Error Estimates of Lowest Order Raviart-Thomas Mixed Finite Element Methods for Bilinear Optimal Control Problems , 2012 .

[16]  J. Nordbotten,et al.  A combined finite element–finite volume framework for phase-field fracture , 2019, Computer Methods in Applied Mechanics and Engineering.

[17]  E. Casas,et al.  Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semiline , 1996 .

[18]  Yunqing Huang,et al.  Superconvergence of triangular Raviart-Thomas mixed finite element methods for a bilinear constrained optimal control problem , 2013, Comput. Math. Appl..

[19]  Zhaojie Zhou,et al.  Finite element approximation of time fractional optimal control problem with integral state constraint , 2021, AIMS Mathematics.

[20]  Yanping Chen,et al.  Error estimates of fully discrete mixed finite element methods for semilinear quadratic parabolic optimal control problem , 2010 .

[21]  Dongyang Shi,et al.  An efficient NFEM for optimal control problems governed by a bilinear state equation , 2019, Comput. Math. Appl..

[22]  So-Hsiang Chou,et al.  Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems , 2007, SIAM J. Numer. Anal..

[23]  Wenbin Liu,et al.  Local A Posteriori Error Estimates for Convex Boundary Control Problems , 2009, SIAM J. Numer. Anal..

[24]  Fredi Tröltzsch,et al.  Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem , 2002, Comput. Optim. Appl..

[25]  R. Eymard,et al.  A Comparative Study of Characteristic Finite Element and Characteristic Finite Volume Methods for Convection-Diffusion-Reaction Problems on Triangular Grids , 2019, Applied Science and Engineering Progress.

[26]  Dan Tiba,et al.  ERROR ESTIMATES IN THE APPROXIMATION OF OPTIMIZATION PROBLEMS GOVERNED BY NONLINEAR OPERATORS , 2001 .

[27]  Panagiotis Chatzipantelidis,et al.  A finite volume method based on the Crouzeix–Raviart element for elliptic PDE's in two dimensions , 1999, Numerische Mathematik.

[28]  Nianyu Yi,et al.  A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations , 2008, SIAM J. Numer. Anal..

[29]  T. Geveci,et al.  On the approximation of the solution of an optimal control problem governed by an elliptic equation , 1979 .

[30]  Fredi Tröltzsch,et al.  Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control Problem , 1996 .

[31]  Michael Hinze,et al.  A Variational Discretization Concept in Control Constrained Optimization: The Linear-Quadratic Case , 2005, Comput. Optim. Appl..

[32]  Franck Boyer,et al.  Finite Volume Method for 2D Linear and Nonlinear Elliptic Problems with Discontinuities , 2008, SIAM J. Numer. Anal..

[33]  Shuhua Zhang,et al.  L∞-error estimates of rectangular mixed finite element methods for bilinear optimal control problem , 2017, Appl. Math. Comput..

[34]  Richard S. Falk,et al.  Approximation of a class of optimal control problems with order of convergence estimates , 1973 .