期刊文献+
任意字段
题名或关键词
题名
关键词
摘要
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息
共找到3篇文章
< 1 >
每页显示 20 50 100
已选0条
引用分析
参考文献
引证文献
 统计分析
检索结果
已选文献
显示方式：
Supercloseness of the Divergence-Free Finite Element Solutions on Rectangular Grids 认领 引用 被引量：4
1
作者 Yunqing Huang Shangyou Zhang 《Communications in Mathematics and Statistics》 2013年第2期143-162,共20页
By the standard theory,the stable Qk+1,k−Qk,k+1/Qdck divergence-free element converges with the optimal order of approximation for the Stokes equations,but only order k for the velocity in H1-norm and the pressure in ... By the standard theory,the stable Qk+1,k−Qk,k+1/Qdck divergence-free element converges with the optimal order of approximation for the Stokes equations,but only order k for the velocity in H1-norm and the pressure in L2-norm.This is due to one polynomial degree less in y direction for the first component of velocity,which is a Qk+1,k polynomial of x and y.In this manuscript,we will show by supercloseness of the divergence free element that the order of convergence is truly k+1,for both velocity and pressure.For special solutions(if the interpolation is also divergence-free),a two-order supercloseness is shown to exist.Numerical tests are provided confirming the accuracy of the theory. 展开更多
关键词 Mixed finite element Stokes equations Divergence-free element Quadrilateral element Rectangular grids Supercloseness Superconvergence
Finite-difference calculation of traveltimes based on rectangular grid 认领 引用 被引量：2
2
作者 LI Zhen-chun +7 位作者 LIU Yu-lian ZHANG Jian-lei MA Zai-tian WANG Hua-zhong 《Acta Seismologica Sinica(English Edition)》 2004年第6期707-714,共8页
To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to... To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method. 展开更多
关键词 finite-difference eikonal equation first-arrival traveltime rectangular grid Kirchhoff prestack depth migration Marmousi model
暂未订购 下载PDF
Interpolated Galerkin Finite Elements on Rectangular and Cuboid Meshes for the Biharmonic Equation 认领 引用
3
作者 Mengjiao Pan Tatyana Sorokina Shangyou Zhang 《Communications on Applied Mathematics and Computation》 EI CSCD 2026年第2期765-777,共13页
A new Galerkin finite element for the biharmonic equation is constructed on 2D rectangular and 3D cuboid meshes.In this C1-Qk(k≥4)interpolated Galerkin finite element construction,all unknowns associated with t... A new Galerkin finite element for the biharmonic equation is constructed on 2D rectangular and 3D cuboid meshes.In this C1-Qk(k≥4)interpolated Galerkin finite element construction,all unknowns associated with the interior of each element are determined by the direct interpolation of the right-hand-side function,and the rest of the unknowns,associated with the boundary of each element,are determined by solving the remaining linear equations of the Galerkin projection.In comparison with the traditional finite element method in two dimensions,our method reduces the number of unknowns from O(k2)to O(k).Additionally,the method reduces the condition number drastically as it requires only 1%of the computer time,compared with the standard finite elements,in several numerical tests.We prove the existence and uniqueness of the solution and the optimal order of convergence.We confirm the theory by numerical tests in two dimensions and three dimensions. 展开更多
关键词 Finite element Interpolated finite element Rectangular grid Biharmonic equation Tensor product
已选0条
引用分析
参考文献
引证文献
 统计分析
检索结果
已选文献
上一页 1 下一页 到第 页
在线咨询 使用帮助 返回顶部 意见反馈