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| 1 | Computing the lower and upper bounds of Laplace eigenvalue problem:by combining conforming and nonconforming finite element methods显示文摘We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the eigenvalue.Additionally,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented.Thus,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once.Some numerical results are also presented to demonstrate our theoretical analysis. | LUO FuSheng LIN Qun XIE HeHu | 2012 | Science China Mathematics2012，55，5： | 10 |
| 2 | A full multigrid method for nonlinear eigenvalue problems显示文摘We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method. | JIA ShangHui XIE HeHu XIE ManTing XU Fei | 2016 | Science China Mathematics2016，59，10： | 7 |
| 3 | A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM显示文摘一个 cascadic multigrid 方法基于 multilevel 修正计划为特征值问题被建议。与这个新计划,在最好的空间的一个特征值问题能被线性变光滑的步在一系列 multilevel 上解决在特殊最粗糙的空格的有限元素空格和非线性的改正步。一旦有限元素空格的顺序和弄平步的数字适当地被选择,有最佳的计算工作的最佳的集中率能被获得。一些数字实验被介绍验证我们的理论分析。 | Xiaole Han Hehu Xie Fei Xu | 2017 | Journal of Computational Mathematics2017，35，1： | 3 |
| 4 | Spectral methods for weakly singular Volterra integral equations with pantograph delays显示文摘 | Ran ZHANG Benxi ZHU Hehu XIE | 2013 | Frontiers of Mathematics in China2013，8，2： | 2 |
| 5 | A posteriori error estimator for eigenvalue problems by mixed finite element method显示文摘In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments. | JIA ShangHui CHEN HongTao XIE HeHu | 2013 | Science China Mathematics2013，56，5： | 2 |
| 6 | Metric tensors for the interpolation er- ror and its gradient in Lp norm 显示文摘 | Xie Hehu Yin Xiaoho | 2014 | Journal of Computational Physics2014，256，： | 1 |
| 7 | The Weak Galerkin Method for Elliptic Eigenvalue Problems显示文摘This article is devoted to studying the application of the weak Galerkin(WG)finite element method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds.The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions.The non-conforming finite element space of the WG method is the key of the lower bound property.It also makes the WG method more robust and flexible in solving eigenvalue problems.We demonstrate that the WG method can achieve arbitrary high convergence order.This is in contrast with existing nonconforming finite element methods which can provide lower bound approximations by linear finite elements.Numerical results are presented to demonstrate the efficiency and accuracy of the theoretical results. | Qilong Zhai Hehu Xie Ran Zhang Zhimin Zhang | 2019 | Communications in Computational Physics2019，26，6： | 1 |
| 8 | Nonconforming Finite Element Method for the Transmission Eigenvalue Problem显示文摘In this paper,we analyze a nonconforming finite element method for the computation of transmission eigenvalues and the corresponding eigenfunctions.The error estimates of the eigenvalue and eigenfunction approximation are given,respectively.Finally,some numerical examples are provided to validate the theoretical results. | Xia Ji Yingxia Xi Hehu Xie | 2017 | Advances in Applied Mathematics and Mechanics2017，9，1： | 0 |
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