In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary Benard problem under the pointwise control constraint. The states and co-states a...In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary Benard problem under the pointwise control constraint. The states and co-states are approximated by polynomial functions of lowest- order mixed finite element space or piecewise linear functions and control is approximated by piecewise constant functions. We give the a posteriori error estimates for the control, the states and co-states.展开更多
This study examines the Benard convection of an infinite horizontal porous layer permeated by an incompressible thermally conducting viscous fluid in the presence of Coriolis forces. The porous layer is controlled by ...This study examines the Benard convection of an infinite horizontal porous layer permeated by an incompressible thermally conducting viscous fluid in the presence of Coriolis forces. The porous layer is controlled by the Brinkman model. Analytical and numerical solutions are obtained for the cases of stationary convection and overstability. The critical thermal Rayleigh numbers are obtained for different values of the permeability of porous medium, Chandrasekhar number and Taylor number for different boundary conditions. The related eigenvalue problem is solved using the Chebyshev polynomial Tau method.展开更多
In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximat...In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L^∞-norm and optimal error estimates in L^2-norm.展开更多
文摘In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary Benard problem under the pointwise control constraint. The states and co-states are approximated by polynomial functions of lowest- order mixed finite element space or piecewise linear functions and control is approximated by piecewise constant functions. We give the a posteriori error estimates for the control, the states and co-states.
文摘This study examines the Benard convection of an infinite horizontal porous layer permeated by an incompressible thermally conducting viscous fluid in the presence of Coriolis forces. The porous layer is controlled by the Brinkman model. Analytical and numerical solutions are obtained for the cases of stationary convection and overstability. The critical thermal Rayleigh numbers are obtained for different values of the permeability of porous medium, Chandrasekhar number and Taylor number for different boundary conditions. The related eigenvalue problem is solved using the Chebyshev polynomial Tau method.
基金the Research Fund for Doctoral Program of High Education by China State Education Ministry under the Grant 2005042203
文摘In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L^∞-norm and optimal error estimates in L^2-norm.
