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In this article, an optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier,the optimality system is obtained. The derived optimal system becomes coupled, non-symmetric partial differential equations. For discretizations and implementations, the finite element multigrid V -cycle is employed.
The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed.
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참고문헌 (24)
참고문헌 신청
A. Borzi / 2000 / The numerical solution of the steady state solid fuel ignition model and its optimal control / SIAM J. Sci. Comput. 22 (1) : 263 ~ 284
A. Borzi / 2002 / Accuracy and convergence properties of the finite difference multigrid solution of an optimal control optimality system / SIAM J. Control Optim. 41 (5) : 14
A. Borzi / 2003 / Multigrid methods for parabolic distributed optimal control problems / J. Comput. Appl. Math. 157 (2) : 365 ~ 382
A. H. Schatz / 1974 / An observation concerning Ritz-Galerkin methods with indefinite bilinear forms / Math. Comp. 28 : 959 ~ 962
J. H. Bramble / 1988 / The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems / Math. Comp. 51 (184) : 389 ~ 414
A. Borzi / 2002 / Accuracy and convergence properties of the finite difference multigrid solution of an optimal control optimality system / SIAM J. Control Optim. 41 (5) : 14
A. Borzi / 2003 / Multigrid methods for parabolic distributed optimal control problems / J. Comput. Appl. Math. 157 (2) : 365 ~ 382
A. H. Schatz / 1974 / An observation concerning Ritz-Galerkin methods with indefinite bilinear forms / Math. Comp. 28 : 959 ~ 962
J. H. Bramble / 1988 / The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems / Math. Comp. 51 (184) : 389 ~ 414
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