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| 1 | A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations显示文摘In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem is presented.We obtain a posteriori error estimates of the approximated solutions for both the state and the control. | CHEN YanPing HUANG YunQing YI NianYu | 2008 | Science China Mathematics2008，51，8： | 7 |
| 2 | High order compact schemes for gradient approximation显示文摘In this paper, we propose three gradient recovery schemes of higher order for the linear interpolation. The first one is a weighted averaging method based on the gradients of the linear interpolation on the uniform mesh, the second is a geometric averaging method constructed from the gradients of two cubic interpolation on macro element, and the last one is a local least square method on the nodal patch with cubic polynomials. We prove that these schemes can approximate the gradient of the exact solution on the symmetry points with fourth order. In particular, for the uniform mesh, we show that these three schemes are the same on the considered points. The last scheme is more robust in general meshes. Consequently, we obtain the superconvergence results of the recovered gradient by using the aforementioned results and the supercloseness between the finite element solution and the linear interpolation of the exact solution. Finally, we provide several numerical experiments to illustrate the theoretical results. | Huang YunQing Liang Qin Yi NianYu | 2010 | Science China Mathematics2010，53，7： | 3 |
| 3 | Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation显示文摘Anisotropic meshes are known to be well-suited for problems which exhibit anisotropic solution features.Defning an appropriate metric tensor and designing an efcient algorithm for anisotropic mesh generation are two important aspects of the anisotropic mesh methodology.In this paper,we are concerned with the natural metric tensor for use in anisotropic mesh generation for anisotropic elliptic problems.We provide an algorithm to generate anisotropic meshes under the given metric tensor.We show that the inverse of the anisotropic difusion matrix of the anisotropic elliptic problem is a natural metric tensor for the anisotropic mesh generation in three aspects:better discrete algebraic systems,more accurate fnite element solution and superconvergence on the mesh nodes.Various numerical examples demonstrating the efectiveness are presented. | HUANG YunQing SU YiFan WEI HuaYi YI NianYu | 2013 | Science China Mathematics2013，56，12： | 2 |
| 4 | A LEGENDRE GALERKIN SPECTRAL METHOD FOR OPTIMAL CONTROL PROBLEMS显示文摘这份报纸认为 Legendre 是 Galerkin 光谱为非强迫的最佳的控制问题的近似。作者导出 posteriori 错误估计为光谱最佳的控制的近似计划问题。由选择适当基础功能, discretization 方程的生硬矩阵是稀少的。并且作者使用快 Legendre 变换改进这个方法的效率。表明我们的理论结果的二个数字实验被介绍。 | Yanping CHEN Nianshi XIA Nianyu YI | 2011 | Journal of Systems Science & Complexity2011，24，4： | 1 |
| 5 | VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY PARABOLIC EQUATIONS显示文摘This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations.The state and co-state are approximated by RaviartThomas mixed finite element spaces,and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control.A priori error estimates are derived for the state,the co-state,and the control.Some numerical examples are presented to confirm the theoretical investigations. | CHEN Yanping HOU Tianliang YI Nianyu | 2013 | Journal of Systems Science & Complexity2013，26，6： | 1 |
| 6 | The Superconvergent Cluster Recovery Method显示文摘 | Yunqing Huang Nianyu Yi | 2010 | Journal of Scientific Computing2010，，3： | 1 |
| 7 | SomeWeighted Averaging Methods for Gradient Recovery显示文摘We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging methods.It is shown analytically that the harmonic averaging yields a superconvergent gradient for any mesh in one-dimension and the rectangular mesh in two-dimension.Numerical results indicate that these new weighted averaging methods are better recovered gradient approaches than the simple averaging and geometry averaging methods under triangular mesh. | Yunqing Huang Kai Jiang Nianyu Yi | 2012 | Advances in Applied Mathematics and Mechanics2012，4，2： | 0 |
| 8 | RECOVERY BASED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATION IN 2D显示文摘We design and numerically validate a recovery based linear finite element method for solving the biharmonic equation.The main idea is to replace the gradient operator▽on linear finite element space by G(▽)in the weak formulation of the biharmonic equation,where G is the recovery operator which recovers the piecewise constant function into the linear finite element space.By operator G,Laplace operator△is replaced by▽·G(▽).Furthermore,the boundary condition on normal derivative▽u-n is treated by the boundary penalty method.The explicit matrix expression of the proposed method is also introduced.Numerical examples on the uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed method. | Yunqing Huang Huayi Wei Wei Yang Nianyu Yi | 2020 | Journal of Computational Mathematics2020，38，1： | 0 |
| 9 | A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrodinger Equation显示文摘Abstract.In this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic form.We use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time discretization.Both mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta method.Numerical examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations. | Jun Yang Nianyu Yi | 2023 | Advances in Applied Mathematics and Mechanics2023，15，3： | 0 |
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