A MULTIGRID METHOD FOR AN OPTIMAL CONTROL PROBLEM OF A DIFFUSION-CONVECTION EQUATION

키워드

참고문헌 (24)

1. Z.-Z. Bai, "On inexact preconditioners for nonsymmetric matrices", SIAM J. Sci. Comput., 26(5), pp.1710~1724 (2005)
2. R. Becker, "Optimal control of the convection-diffusion equation using stabilized finite element methods", Numer. Math., 106(3), pp.349~367 (2007)
3. P. B. Bochev, "Least-squares finite element methods for optimality systems arising in optimization and control problems", SIAM J. Numer. Anal., 43(6), pp.2517~2543 (2006)
4. A. Borzi, "Multigrid methods for parabolic distributed optimal control problems", J. Comput. Appl. Math., 157(2), pp.365~382 (2003)
5. A. Borzi, "The numerical solution of the steady state solid fuel ignition model and its optimal control", SIAM J. Sci. Comput., 22(1), pp.263~284 (2000)
6. A. Borzi, "Accuracy and convergence properties of the finite difference multigrid solution of an optimal control optimality system", SIAM J. Control Optim., 41(5), pp.1477~1497 (2002)
7. J. H. Bramble, "Multigrid Methods, Pitman Res. Notes Math, Ser. 294" (1993), John Wiley
8. J. H. Bramble, "Uniform convergence of multigrid V -cycle iterations for indefinite and nonsymmetric problems", SIAM J. Numer. Anal., 31(6), pp.1746~1763 (1994)
9. J. H. Bramble, "New estimates for multilevel algorithms including the V -cycle", Math. Comp., 60(202), pp.447~471 (1993)
10. J. H. Bramble, "The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems", Math. Comp., 51(184), pp.389~414 (1988)
11. J. H. Bramble, "The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms", Math. Comp., 56(193), pp.1~34 (1991)
12. S. C. Brenner, "Convergence of the multigrid V -cycle algorithm for second-order boundary value problems without full elliptic regularity", Math. Comp., 71(238), pp.507~525 (2002)
13. S. C. Brenner, "The mathematical Theory of Finite Element Methods" (2002), Springer-Verlag
14. L. C. Evans, "Partial Differential Equations, Graduate Studies in Mathematics, 19" (1998), American Mathematical Society
15. J. L. Guermond, "Stabilization of Galerkin approximations of transport equations by subgrid modeling", M2AN Math. Model. Numer. Anal., 33(6), pp.1293~1316 (1999)
16. M. D. Gunzburger, "Perspectives in Flow Control and Optimization, Advances in Design and Control, 5" (2003), Society for Industrial and Applied Mathematics (SIAM)
17. M. D. Gunzburger, "Analysis, approximation, and computation of a coupled solid", fluid temperature control problem, 1994, pp.118(1), 133~152
18. M. D. Gunzburger, "Analysis and approximation of optimal control problems for first-order elliptic systems in three dimensions", Appl. Math. Comput., 100(1), pp.49~70 (1999)
19. W. Hackbusch, "Multigrid Methods and Applications, Springer Series in Computational Mathematics, 4" (1985), Springer-Verlag
20. J. L. Lions, "Optimal Control of Systems Governed by Partial Differential Equations" (1971), Springer-Verlag
21. P. Neittaanmaki, "Optimal Control of Nonlinear Parabolic Systems" (1994), Marcel Dekker
22. M. H. van Raalte, "Two-level multigrid analysis for the convectiondiffusion equation discretized by a discontinuous Galerkin method", Numer. Linear Algebra Appl., 12(5), pp.563~584 (2005)
23. A. H. Schatz, "An observation concerning Ritz-Galerkin methods with indefinite bilinear forms", Math. Comp., 28, pp.959~962 (1974)
24. J. Wang, "Convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems", SIAM J. Numer. Anal., 30(1), pp.275~285 (1993)

관련 논문AI추천