Relations of the 3D multi-directional derivatives are studied in this paper. These relations are applied to a geeral second-order linear elliptical operator and the corresponding expression are obtained. These relatio...Relations of the 3D multi-directional derivatives are studied in this paper. These relations are applied to a geeral second-order linear elliptical operator and the corresponding expression are obtained. These relations and expressions play important roles in the meshless finite point method.展开更多
In this paper,we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations.The state and co-state are approximated by the lowest order Raviart-...In this paper,we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations.The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We derive L2 and H−1-error estimates both for the control variable and the state variables.Finally,a numerical example is given to demonstrate the theoretical results.展开更多
基金Supported by the National Natural Science Foundation of China 1060100910701014+1 种基金10871029)the Foundation of China Academy of Engineering Physics (2007B09008)
文摘Relations of the 3D multi-directional derivatives are studied in this paper. These relations are applied to a geeral second-order linear elliptical operator and the corresponding expression are obtained. These relations and expressions play important roles in the meshless finite point method.
基金supported by National Natural Science Foundation of China(Grant No.11526036)Scientific and Technological Developing Scheme of Jilin Province(Grant No.20160520108JH).
文摘In this paper,we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations.The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We derive L2 and H−1-error estimates both for the control variable and the state variables.Finally,a numerical example is given to demonstrate the theoretical results.
