检索结果-内蒙古大学图书馆

Superconvergence analysis of adaptive finite element method based on the bubble-type mesh generation

APPLIED MATHEMATICS LETTERS 2019年 98卷 322-328页

作者： Li, Xiangrong Zhang, Weiwei Nie, Yufeng Northwestern Polytech Univ Res Ctr Computat Sci Xian 710129 Shaanxi Peoples R China

This paper studies the superconvergence phenomena appearing in bubble-type adaptive finite element process. Based on a mesh condition derived from the bubble-type mesh generation, a superconvergence result of parallel to u(h) - u(I)parallel to(1, Omega) is obtained. Further, under the recovered gradient methods, a superconvergence estimation of bubble-type adaptive procedure is established. Theoretically, the reason behind the appearance of superconvergence in bubble-type adaptive procedure is justified. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Superconvergence adaptive finite element method Mesh generation

来源：评论

学校读者我要写书评

暂无评论

An adaptive finite element method for parabolic interface problems with nonzero flux jumps

引用

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2021年 82卷 97-112页

作者： Ray, Tanushree Sinha, Rajen Kumar Indian Inst Technol Guwahati Dept Math Gauhati 781039 India

We consider an adaptive finite element method for solving parabolic interface problems with nonzero flux jumps in a two-dimensional convex polygonal domain. We use continuous, piecewise linear functions for the approximation of the spatial variable whereas the backward Euler method is employed for the time discretization. The reliability bound of the estimator is derived in terms of the error indicators using the energy argument. An efficiency bound for the local error in terms of the space error indicator is also established. We provide an adaptive algorithm which reduces the error indicators below any given tolerance within a finite number of steps. Our numerical experiment reveals the performance of the derived error indicators with satisfactory numerical results. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Parabolic interface problem adaptive finite element method A posteriori error estimates

来源：评论

学校读者我要写书评

暂无评论

A multilevel correction adaptive finite element method for Kohn-Sham equation

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2018年 355卷 436-449页

作者： Hu, Guanghui Xie, Hehu Xu, Fei Univ Macau Dept Math Macau Peoples R China UM Zhuhai Res Inst Zhuhai Guangdong Peoples R China Chinese Acad Sci Acad Math & Syst Sci ICMSEC LSEC Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China Beijing Univ Technol Beijing Inst Sci & Engn Comp Beijing 100124 Peoples R China

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Density functional theory Kohn-Sham equation Multilevel correction adaptive finite element method

来源：评论

学校读者我要写书评

暂无评论

A convergent adaptive finite element method for elliptic Dirichlet boundary control problems

引用

IMA JOURNAL OF NUMERICAL ANALYSIS 2019年第4期39卷 1985-2015页

作者： Gong, Wei Liu, Wenbin Tan, Zhiyu Yan, Ningning Chinese Acad Sci Natl Ctr Math & Interdisciplinary Sci State Key Lab Sci & Engn Comp Inst Computat MathAcad Math & Syst Sci Beijing 100190 Peoples R China Univ Kent Kent Business Sch Canterbury CT2 7PE Kent England Hong Kong Baptist Univ Dept Math Kowloon Tong Hong Kong Peoples R China Chinese Acad Sci Acad Math & Syst Sci Inst Syst Sci NCMISLSEC Beijing 100190 Peoples R China

This paper concerns the adaptive finite element method for elliptic Dirichlet boundary control problems in the energy space. The contribution of this paper is twofold. First, we rigorously derive efficient and reliable a posteriori error estimates for finite element approximations of Dirichlet boundary control problems. As a by-product, a priori error estimates are derived in a simple way by introducing appropriate auxiliary problems and establishing certain norm equivalence. Secondly, for the coupled elliptic partial differential system that resulted from the first-order optimality system, we prove that the sequence of adaptively generated discrete solutions including the control, the state and the adjoint state, guided by our newly derived a posteriori error indicators, converges to the true solution along with the convergence of the error estimators. We give some numerical results to confirm our theoretical findings.

关键词： optimal control problem elliptic equation Dirichlet boundary control energy space adaptive finite element method convergence

来源：评论

学校读者我要写书评

暂无评论

QUASI-OPTIMALITY OF AN adaptive finite element method FOR CATHODIC PROTECTION

引用

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 2019年第5期53卷 1645-1665页

作者： Li, Guanglian Xu, Yifeng Imperial Coll London Dept Math London SW7 2AZ England Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Shanghai Normal Univ Sci Comp Key Lab Shanghai Univ Shanghai 200234 Peoples R China

In this work, we derive a reliable and efficient residual-typed error estimator for the finite element approximation of a 2D cathodic protection problem governed by a steady-state diffusion equation with a nonlinear boundary condition. We propose a standard adaptive finite element method involving the Dorfler marking and a minimal refinement without the interior node property. Furthermore, we establish the contraction property of this adaptive algorithm in terms of the sum of the energy error and the scaled estimator. This essentially allows for a quasi-optimal convergence rate in terms of the number of elements over the underlying triangulation. Numerical experiments are provided to confirm this quasi-optimality.

关键词： Cathodic protection nonlinear boundary condition a posteriori error estimator adaptive finite element method quasi-optimality

来源：评论

学校读者我要写书评

暂无评论

A GOAL-ORIENTED adaptive finite element method WITH CONVERGENCE RATES

引用

SIAM JOURNAL ON NUMERICAL ANALYSIS 2009年第2期47卷 861-886页

作者： Mommer, Mario S. Stevenson, Rob Univ Heidelberg Interdisciplinary Ctr Sci Comp IWR D-69120 Heidelberg Germany Univ Amsterdam Korteweg de Vries Inst Math NL-1018 TV Amsterdam Netherlands

An adaptive finite element method is analyzed for approximating functionals of the solution of symmetric elliptic second order boundary value problems. We show that the method converges and derive a favorable upper bound for its convergence rate and computational complexity. We illustrate our theoretical findings with numerical results.

关键词： adaptive finite element method convergence rates computational complexity quantity of interest a posteriori error estimators

来源：评论

学校读者我要写书评

暂无评论

An optimal adaptive finite element method for the Stokes problem

引用

SIAM JOURNAL ON NUMERICAL ANALYSIS 2008年第2期46卷 747-775页

作者： Kondratyuk, Yaroslav Stevenson, Rob Humboldt Univ Dept Math D-10099 Berlin Germany Korteweg de Vries Inst Math NL-1018 TV Amsterdam Netherlands

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the ( elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems is a Stokes-type problem, with the pressure being sought in the current trial space and the divergence-free constraint being reduced to orthogonality of the divergence to this trial space. Such a problem is still continuous in the velocity field. In the middle loop, its solution is approximated using the Uzawa scheme. In the innermost loop, the solution of the elliptic system for the velocity field that has to be solved in each Uzawa iteration is approximated by an adaptive finite element method.

关键词： adaptive finite element method convergence rates computational complexity a posteriori error estimators Uzawa iteration Stokes equations

来源：评论

学校读者我要写书评

暂无评论

ANALYSIS OF AN adaptive finite element method FOR RECOVERING THE ROBIN COEFFICIENT

引用

SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2015年第2期53卷 622-644页

作者： Xu, Yifeng Zou, Jun Shanghai Univ Dept Math Sci Comp Key Lab Shanghai 200234 Peoples R China Shanghai Univ Shanghai Normal Univ Inst Computat Sci E Shanghai 200234 Peoples R China Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China

Based on a new a posteriori error estimator, an adaptive finite element method is proposed for recovering the Robin coefficient involved in a diffusion system from some boundary measurement. The a posteriori error estimator cannot be derived for this ill-posed nonlinear inverse problem as was done for the existing a posteriori error estimators for direct problems. Instead, we shall derive the a posteriori error estimator from our convergence analysis of the adaptive algorithm. We prove that the adaptive algorithm guarantees a convergent subsequence of discrete solutions in an energy norm to some exact triplet (the Robin coefficient, state and costate variables) determined by the optimality system of the least-squares formulation with Tikhonov regularization for the concerned inverse problem. Some numerical results are also reported to illustrate the performance of the algorithm.

关键词： Robin inverse problem a posteriori error estimates adaptive finite element method

来源：评论

学校读者我要写书评

暂无评论

Convergence and quasi-optimality of an adaptive finite element method for nonmonotone quasi-linear elliptic problems on L2 errors

引用

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2023年 139卷 38-56页

作者： Guo, Liming Bi, Chunjia Xinyang Normal Univ Sch Math & Stat Xinyang 464000 Peoples R China Yantai Univ Sch Math & Informat Sci Yantai 264005 Peoples R China

In this paper, we establish the convergence and quasi-optimality of an adaptive finite element method for nonmonotone elliptic problems on L2 errors for a sufficiently fine initial mesh. Although additional refinements are needed to keep the meshes sufficiently mildly graded, it does not affect the convergence and quasi-optimality of the adaptive finite element method presented in this paper. Our theoretical results are verified by some numerical examples.

关键词： adaptive finite element method Convergence Quasi-optimality Nonmonotone elliptic problems L2 errors

来源：评论

学校读者我要写书评

暂无评论

Multilevel correction adaptive finite element method for solving nonsymmetric eigenvalue problems

引用

ADVANCES IN COMPUTATIONAL MATHEMATICS 2021年第2期47卷 1-30页

作者： Xu, Fei Yue, Meiling Zheng, Bin Beijing Univ Technol Beijing Inst Sci & Engn Comp Fac Sci Beijing 100124 Peoples R China Beijing Technol & Business Univ Sch Math & Stat Beijing 100048 Peoples R China

Large-scale nonsymmetric eigenvalue problems are common in various fields of science and engineering computing. However, their efficient handling is challenging, and research on their solution algorithms is limited. In this study, a new multilevel correction adaptive finite element method is designed for solving nonsymmetric eigenvalue problems based on the adaptive refinement technique and multilevel correction scheme. Different from the classical adaptive finite element method, which requires solving a nonsymmetric eigenvalue problem in each adaptive refinement space, our approach requires solving a symmetric linear boundary value problem in the current refined space and a small-scale nonsymmetric eigenvalue problem in an enriched correction space. Since it is time-consuming to solve a large-scale nonsymmetric eigenvalue problem directly in adaptive spaces, the proposed method can achieve nearly the same efficiency as the classical adaptive algorithm when solving the symmetric linear boundary value problem. In addition, the corresponding convergence and optimal complexity are verified theoretically and demonstrated numerically.

关键词： Nonsymmetric eigenvalue problems adaptive finite element method Multilevel correction method Convergence and optimality complexity

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：