L ∞-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations
Tóm tắt
Từ khóa
Tài liệu tham khảo
Schatz, A.H. and Wahlbin, L.B., Pointwise Error Estimates for Diffferences in Piecewise Linear Finite Element Approximations, SIAM J. Numer. Anal., 2003, no. 46, pp. 2149–2160.
Schatz, A.H. and Wahlbin, L.B., Asymptotically Exact a Posteriori Error Estimators for the Pointwise Gradient Error on Each Element in Irregular Meshes. II. The Piecewise Linear Case, Math. Comp., 2004, no. 73, pp. 517–523.
Kwon, Y. and Milner, F.A., L ∞-Error Estimates for Mixed Methods for Semilinear Second-Order Elliptic Equations, SIAM J. Numer. Anal., 1988, no. 25, pp. 46–53.
Brunner, H. and Yan, N.N., Finite Element Methods for Optimal Control Problems Governed by Integral Equations and Integro-Differential Equations, Appl. Numer. Math., 2003, no. 47, pp. 173–187.
Falk, F.S., Approximation of a Class of Optimal Control Problems with Order of Convergence Estimates, J. Math. Anal. Appl., 1973, no. 44, pp. 28–47.
Gunzburger, M.D. and Hou, S.L., Finite Dimensional Approximation of a Class of Constrained Nonlinear Control Problems, SIAM J. Control Optim., 1996, no. 34, pp. 1001–1043.
Meyer, C. and Rösch, A., L ∞-Error Estimates for Approximated Optimal Control Problems, SIAM J. Control Optim., 2005, no. 5, pp. 1636–1649.
Liu, W.B. and Yan, N.N., A Posteriori Error Estimates for Control Problems Governed by Stokes’ Equations, SIAM J. Numer. Anal., 2003, no. 40, pp. 1850–1869.
Liu, W.B. and Yan, N.N., A Posteriori Error Estimates for Distributed Convex Optimal Control Problems, Adv. Comput. Math., 2001, no. 15, pp. 285–309.
Raviart, P.A. and Thomas, J.M., A Mixed Finite Element Method for 2nd Order Elliptic Problems, Lect. Notes Math., 1977, no. 660, pp. 292–315.
Hou, L. and Turner, J.C., Analysis and Finite Element Approximation of an Optimal Control Problem in Electrochemistry with Current Density Controls, Numer. Math., 1995, no. 71, pp. 289–315.
Chen, Y. and Liu, W.B., Error Estimates and Superconvergence of Mixed Finite Element for Quadratic Optimal Control, Int. J. Numer. Anal. Model., 2006, no. 3, pp. 311–321.
Chen, Y. and Liu, W.B., A Posteriori Error Estimates for Mixed Finite Element Solutions of Convex Optimal Control Problems, J. Comp. Appl.Math., 2008, no. 211, pp. 76–89.
Arada, N., Casas, E. and Tröltzsch, F., Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem, Comp. Optim. Appl., 2002, no. 23, pp. 201–229.
Lions, J.L., Optimal Control of Systems Governed by Partial Differential Equations, Berlin: Springer, 1971.
Chen, Y., Superconvergence of Optimal Control Problems by Rectangular Mixed Finite Element Methods, Math. Comp., 2008, no. 77, pp. 1269–1291.
Lu, Z.L. and Zhang, H.W.,A V-Cycle Multigrid Method for a Viscoelastic Fluid Flow Satisfying an Oldroyd-B-Type Constitutive Equation, Sib. Zh. Vych. Mat., 2008, vol. 11, no. 1, pp. 83–94.
Aleksandrov, V.M., Iterative Method for Computing Time Optimal Control in Real Time Mode, Sib. Zh. Vych. Mat., 2007, vol. 10, no. 1, pp. 1–28.
Miliner, F.A., Mixed Finite Element Methods for Quasilinear Second-Order Elliptic Problems, Math. Comp., 1985, no. 44, pp. 303–320.
Chen, Y. and Liu, W.B., Error Estimates and Superconvergence of Mixed Finite Elements for Quadratic Optimal Control, Int. J. Numer. Anal. Model., 2006, no. 3, pp. 311–321.
Scholz, R., A Remark on the Rate of Convergence for a Mixed Finite Element Method for Second Order Problems, Numer. Func. Anal. Optim., 1982, no. 4, pp. 269–277.
Xing, X. and Chen, Y., L ∞-Error Estimates for General Optimal Control Problem by Mixed Finite Element Methods, Int. J. Numer. Anal. Model., 2008, no. 5, pp. 441–456.
Li, R. and Liu, W.B., http://circus.math.pku.edu.cn/AFEPack .