In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k...In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k=1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We prove the superconvergence error estimate of h3/2 in L2-norm between the approximated solution and the average L2 projection of the control.Moreover,by the postprocessing technique,a quadratic superconvergence result of the control is derived.展开更多
This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method dev...This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method developed by Klaus Hollig to derive this new idea. First of all, the authors replace the R-function method with transfinite interpolation to build a function which vanishes on boundaries. Secondly, the authors simulate the partial differential equation by directly applying differential opera- tors to basis functions, which is similar to the RBF method rather than Hollig＇s method. These new strategies then make the constructing of bases and the linear system much more straightforward. And as the interpolation is brought in, the design of schemes for solving practical PDEs can be more flexi- ble. This new method is easy to carry out and suitable for simulations in the fields such as graphics to achieve rapid rendering. Especially when the specified much faster than WEB-spline method. precision is not very high, this method performs展开更多
基金supported by National Natural Science Foundation of China(Grant No.10971074)Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20114407110009)
文摘In this paper,we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods.The state and co-state are approximated by the order k=1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We prove the superconvergence error estimate of h3/2 in L2-norm between the approximated solution and the average L2 projection of the control.Moreover,by the postprocessing technique,a quadratic superconvergence result of the control is derived.
基金partially supported by NKBRSF under Grant No.2011CB302404NSFC under Grant Nos. 10871195,10925105,60821002,and 50875027
文摘This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method developed by Klaus Hollig to derive this new idea. First of all, the authors replace the R-function method with transfinite interpolation to build a function which vanishes on boundaries. Secondly, the authors simulate the partial differential equation by directly applying differential opera- tors to basis functions, which is similar to the RBF method rather than Hollig＇s method. These new strategies then make the constructing of bases and the linear system much more straightforward. And as the interpolation is brought in, the design of schemes for solving practical PDEs can be more flexi- ble. This new method is easy to carry out and suitable for simulations in the fields such as graphics to achieve rapid rendering. Especially when the specified much faster than WEB-spline method. precision is not very high, this method performs
