发布求助
文献互助 智能选刊 最新文献

J. Num. Math.最新文献

筛选
英文 中文
Convergence and superconvergence of a nonconforming finite element method for the Stokes problem Stokes问题非协调有限元法的收敛性和超收敛性
J. Num. Math. Pub Date : 2006-06-01 DOI: 10.1515/156939506777443022
S. Mao, Shaochun Chen
{"title":"Convergence and superconvergence of a nonconforming finite element method for the Stokes problem","authors":"S. Mao, Shaochun Chen","doi":"10.1515/156939506777443022","DOIUrl":"https://doi.org/10.1515/156939506777443022","url":null,"abstract":"In this paper, the four-parameter nonconforming finite element proposed in [30] and [19] is analyzed with the framework of Double Set Parameter (DSP) method, then it is applied to the stationary Stokes problem. The element exhibits some features of the well-known Q 1−P 0 element under rectangular meshes. An optimal convergence rate is established for both the velocity and smoothed pressure. Furthermore, the superconvergent approximation between the interpolation of the exact solution and the finite element solution is proved. A superconvergent estimate on the centers of elements and the global superconvergence for the gradient of the velocity and the pressure are derived with the aid of a postprocessing method. Based on the superconvergence property, an asymptotically exact a posteriori estimator of ZZ type is also studied.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124479732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems 不连续伽辽金方法在奇异摄动问题中的局部分析
J. Num. Math. Pub Date : 2006-03-01 DOI: 10.1515/156939506776382157
J. Guzmán
{"title":"Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems","authors":"J. Guzmán","doi":"10.1515/156939506776382157","DOIUrl":"https://doi.org/10.1515/156939506776382157","url":null,"abstract":"We analyze existing discontinuous Galerkin methods on quasi-uniform meshes for singularly perturbed problems. We prove weighted L 2 error estimates. We use the weighted estimates to prove L 2 error estimates in regions where the solution is smooth. We also prove pointwise estimates in these regions.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117111125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 34
Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem Toeplitz矩阵逼近问题的半定二阶锥优化方法
J. Num. Math. Pub Date : 2006-03-01 DOI: 10.1515/156939506776382148
S. Al-Homidan
{"title":"Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem","authors":"S. Al-Homidan","doi":"10.1515/156939506776382148","DOIUrl":"https://doi.org/10.1515/156939506776382148","url":null,"abstract":"The nearest positive semidefinite symmetric Toeplitz matrix to an arbitrary data covariance matrix is useful in many areas of engineering, including stochastic filtering and digital signal processing applications. In this paper, the interior point primal-dual path-following method will be used to solve our problem after reformulating it into different forms, first as a semidefinite programming problem, then into the form of a mixed semidefinite and second-order cone optimization problem. Numerical results, comparing the performance of these methods against the modified alternating projection method will be reported.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116862071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Distributed optimal control of lambda–omega systems 系统的分布式最优控制
J. Num. Math. Pub Date : 2006-03-01 DOI: 10.1515/156939506776382120
A. Borzì, R. Griesse
{"title":"Distributed optimal control of lambda–omega systems","authors":"A. Borzì, R. Griesse","doi":"10.1515/156939506776382120","DOIUrl":"https://doi.org/10.1515/156939506776382120","url":null,"abstract":"The formulation, analysis, and numerical solution of distributed optimal control problems governed by lambda–omega systems is presented. These systems provide a universal model for reaction-diffusion phenomena with turbulent behavior. Existence and regularity properties of solutions to the free and controlled lambda–omega models are investigated. To validate the ability of distributed control to drive lambda–omega systems from a chaotic to an ordered state, a space-time multigrid method is developed based on a new smoothing scheme. Convergence properties of the multigrid scheme are discussed and results of numerical experiments are reported.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123404797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 35
A posteriori error estimates for adaptive finite element discretizations of boundary control problems 边界控制问题自适应有限元离散化的后验误差估计
J. Num. Math. Pub Date : 2006-03-01 DOI: 10.1515/156939506776382139
R. Hoppe, Y. Iliash, C. Iyyunni, N. Sweilam
{"title":"A posteriori error estimates for adaptive finite element discretizations of boundary control problems","authors":"R. Hoppe, Y. Iliash, C. Iyyunni, N. Sweilam","doi":"10.1515/156939506776382139","DOIUrl":"https://doi.org/10.1515/156939506776382139","url":null,"abstract":"We are concerned with an a posteriori error analysis of adaptive finite element approximations of boundary control problems for second order elliptic boundary value problems under bilateral bound constraints on the control which acts through a Neumann type boundary condition. In particular, the analysis of the errors in the state, the co-state, the control, and the co-control invokes an efficient and reliable residual-type a posteriori error estimator as well as data oscillations. The proof of the efficiency and reliability is done without any regularity assumption. Adaptive mesh refinement is realized on the basis of a bulk criterion. The performance of the adaptive finite element approximation is illustrated by a detailed documentation of numerical results for selected test problems.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115091317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 49
A least-squares approximation method for the time-harmonic Maxwell equations 时谐麦克斯韦方程组的最小二乘逼近方法
J. Num. Math. Pub Date : 2005-12-01 DOI: 10.1515/156939505775248347
J. Bramble, T. Kolev, J. Pasciak
{"title":"A least-squares approximation method for the time-harmonic Maxwell equations","authors":"J. Bramble, T. Kolev, J. Pasciak","doi":"10.1515/156939505775248347","DOIUrl":"https://doi.org/10.1515/156939505775248347","url":null,"abstract":"In this paper we introduce and analyze a new approach for the numerical approximation of Maxwell's equations in the frequency domain. Our method belongs to the recently proposed family of negative-norm least-squares algorithms for electromagnetic problems which have already been applied to the electrostatic and magnetostatic problems as well as the Maxwell eigenvalue problem (see [4,5]). The scheme is based on a natural weak variational formulation and does not employ potentials or 'gauge conditions'. The discretization involves only simple, piecewise polynomial, finite element spaces, avoiding the use of the complicated Nédélec elements. An interesting feature of this approach is that it leads to simultaneous approximation of the magnetic and electric fields, in contrast to other methods where one of the unknowns is eliminated and is later computed by differentiation. More importantly, the resulting discrete linear system is well-conditioned, symmetric and positive definite. We demonstrate that the overall numerical algorithm can be efficiently implemented and has an optimal convergence rate, even for problems with low regularity.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115814607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients 具有强不连续和各向异性系数的非对称分层问题的优化Schwarz方法
J. Num. Math. Pub Date : 2005-12-01 DOI: 10.1515/156939505775248338
L. Gerardo-Giorda, F. Nataf
{"title":"Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients","authors":"L. Gerardo-Giorda, F. Nataf","doi":"10.1515/156939505775248338","DOIUrl":"https://doi.org/10.1515/156939505775248338","url":null,"abstract":"In this paper we consider unsymmetric elliptic problems of advection–diffusion–reaction type, with strongly heterogeneous and anisotropic diffusion coefficients. We use non-overlapping Optimized Schwarz Methods (OSM) and we study new interface conditions where only one or two real parameters have to be chosen along the entire interface. Using one real parameter it is possible to design interface conditions of Robin type, whereas the use of two real parameters and of more general interface conditions allows to better take into account the heterogeneities of the medium. The analysis is made at the semi-discrete level, where the equation is discretized in the direction parallel to the interface, and kept continuous in the normal direction. Numerical results are given to validate the proposed interface conditions.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"249 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124748019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
A new sequence of hierarchic prismatic elements satisfying De Rham diagram on hybrid meshes 混合网格上满足De Rham图的一种新的分层棱柱元序列
J. Num. Math. Pub Date : 2005-12-01 DOI: 10.1515/156939505775248329
P. Solín, K. Segeth
{"title":"A new sequence of hierarchic prismatic elements satisfying De Rham diagram on hybrid meshes","authors":"P. Solín, K. Segeth","doi":"10.1515/156939505775248329","DOIUrl":"https://doi.org/10.1515/156939505775248329","url":null,"abstract":"This paper presents a new sequence of affine-equivalent H(curl)- and H(div)-conforming hierarchic prismatic finite elements of arbitrary polynomial degrees, satisfying De Rham diagram on hybrid tetrahedral-prismatic-hexahedral meshes. We also present suitable H(curl)- and H(div)-conforming reference maps that preserve the commutativity of the De Rham diagram.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124410478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
UR Birkhoff interpolation schemes: reduction criterias UR Birkhoff插值格式:约简准则
J. Num. Math. Pub Date : 2005-09-01 DOI: 10.1515/156939505774286111
N. Crainic
{"title":"UR Birkhoff interpolation schemes: reduction criterias","authors":"N. Crainic","doi":"10.1515/156939505774286111","DOIUrl":"https://doi.org/10.1515/156939505774286111","url":null,"abstract":"In this paper we study the UR Birkhoff interpolation schemes and establish several criterias for reducing the complexity of the problem. As an immediate consequence, we characterize all UR Birkhoff schemes which involve no mixed derivative.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124285506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On improvement of the iterated Galerkin solution of the second kind integral equations 第二类积分方程迭代伽辽金解的改进
J. Num. Math. Pub Date : 2005-09-01 DOI: 10.1515/156939505774286139
R. Kulkarni
{"title":"On improvement of the iterated Galerkin solution of the second kind integral equations","authors":"R. Kulkarni","doi":"10.1515/156939505774286139","DOIUrl":"https://doi.org/10.1515/156939505774286139","url":null,"abstract":"For a second kind integral equation with a kernel which is less smooth along the diagonal, an approximate solution obtained by using a method proposed by the author in an earlier paper, is shown to have a higher rate of convergence than the iterated Galerkin solution. The projection is chosen to be either the orthogonal projection or an interpolatory projection onto a space of piecewise polynomials. The size of the system of equations that needs to be solved, in order to compute the proposed solution, remains the same as in the Galerkin method. The improvement of the proposed solution is illustrated by a numerical example.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121219451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信