首页/论文/2006.09573

arXiv 2006.095732020-06-17math.NAcs.NA

A virtual element method for the Steklov eigenvalue problem allowing small edges

Felipe Lepe, David Mora, Gonzalo Rivera, Iván Velásquez

英文摘要：

The aim of this paper is to analyze the influence of small edges in the computation of the spectrum of the Steklov eigenvalue problem by a lowest order virtual element method. Under weaker assumptions on the polygonal meshes, which can permit arbitrarily small edges with respect to the element diameter, we show that the scheme provides a correct approximation of the spectrum and prove optimal error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we report some numerical tests supporting the theoretical results.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients

In this paper, using new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain lower eigenvalue bounds for the Steklov eigenvalue problem with variable coefficients on d-dimensional domains (d = 2,3). In addition, we prove that the corrected eigenvalues asymptotically converge to the exact ones from below whether the eigenfunctions are singular or smooth and whether the eigenvalues are large enough or not. Further, we prove that the corrected eigenvalues still maintain the same convergence order as that of uncorrected eigenvalues. Finally, numerical experiments…

2019-08-24cs.NAmath.NA

通过共形映射求解Steklov特征值问题的数值研究

A Numerical Study of Steklov Eigenvalue Problem via Conformal Mapping

Claremont Graduate University（克莱蒙特研究生大学）；Claremont McKenna College（克莱蒙特门纳学院）

本文提出基于共形映射的谱方法求解二维Steklov特征值问题及其相关形状优化问题，通过傅里叶级数展开将特征函数离散化，并利用梯度上升法寻找最优域以最大化固定面积下的k阶Steklov特征值。

2018-05-04cs.NAmath.NA

A locking-free discontinuous Galerkin method for linear elastic Steklov eigenvalue problem

In this paper, a discontinuous Galerkin finite element method of Nitsche's version for the Steklov eigenvalue problem in linear elasticity is presented. The a priori error estimates are analyzed under a low regularity condition, and the robustness with respect to nearly incompressible materials (locking-free) is proven. Furthermore, some numerical experiments are reported to show the effectiveness and robustness of the proposed method.

2022-12-25cs.NAmath.NA

Guaranteed lower eigenvalue bounds for Steklov operators using conforming finite element methods

For the eigenvalue problem of the Steklov differential operator, by following Liu's approach, an algorithm utilizing the conforming finite element method (FEM) is proposed to provide guaranteed lower bounds for the eigenvalues. The proposed method requires the a priori error estimation for FEM solution to nonhomogeneous Neumann problems, which is solved by constructing the hypercircle for the corresponding FEM spaces and boundary conditions. Numerical examples are also shown to confirm the efficiency of our proposed method.

2023-02-05cs.NAmath.NA

求解 Steklov 特征值问题的弱 Galerkin 有限元方法

The weak Galerkin finite element method for the Steklov eigenvalue problem

本文将弱 Galerkin 有限元方法用于 Steklov 特征值问题，借助非协调有限元空间获得任意高阶且有保证的特征值下界，并通过数值实验验证其准确性。

2024-05-10cs.NAmath.NA

基于移位反迭代的适应性算法用于Steklov特征值问题

An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem

School of Mathematics and Computer Science, Guizhou Normal University（贵州师范大学数学与计算机科学学院）

本文提出并分析了有限元多尺度离散化近似Steklov特征值问题的后验误差估计器，设计了移位反迭代类型的自适应算法，并通过数值实验验证了其效率。

2016-01-07cs.NAmath.NA

更多相关论文收起更多论文

Steklov特征值问题的保证特征值界

Guaranteed eigenvalue bounds for the Steklov eigenvalue problem

CAEP Software Center for High Performance Numerical Simulation（中国工程物理研究院高性能数值模拟软件中心）；LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所、中国科学院系统科学研究所）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Graduate School of Science and Technology, Niigata University（新潟大学理工学研究科）

本文提出改进的特征值估计算法，去除双线性形式正定性要求，采用Crouzeix-Raviart有限元法和定量误差估计，通过数值实验验证计算特征值界精度。

2018-08-24cs.NAmath.NA

一种用于反散射中新型Steklov特征值问题的多网格校正方案

A multigrid correction scheme for a new Steklov eigenvalue problem in inverse scattering

School of Mathematical Sciences, Guizhou Normal University（贵州师范大学数学科学学院）

本文提出一种多网格校正方案，用于求解反散射中新型Steklov特征值问题，通过将细网格有限元空间的特征值问题转化为一系列边界值问题和最粗网格有限元空间的特征值问题，证明系数矩阵对称正定，并给出误差估计。

2018-06-15cs.NAmath.NA

Steklov特征值问题的虚拟元方法后验误差估计

A posteriori error estimates for a Virtual Elements Method for the Steklov eigenvalue problem

Universidad del Bío-Bío（比奥比奥大学）；Universidad de Concepción（康塞普西翁大学）

本文研究了虚拟元方法在Steklov特征值问题中的后验误差分析，提出了一种残差型误差估计器，并通过数值实验验证了其有效性。

2016-09-22cs.NAmath.NA

非自伴斯蒂克洛夫特征值问题的谱指示法

Spectral Indicator Method for A Non-selfadjoint Steklov Eigenvalue Problem

Jinan University（暨南大学）；Michigan Technological University（密歇根理工大学）；University of Maryland Eastern Shore（马里兰东部大学）

本文提出一种高效方法求解非自伴斯蒂克洛夫特征值问题，利用拉格朗日有限元离散，并通过谱扰动理论证明收敛性，采用改进的谱指示法计算复特征值，通过数值例子验证有效性。

2018-04-07cs.NAmath.NA

线性三角有限元对Steklov特征值问题的新的误差估计

New error estimates of linear triangle finite elements for the Steklov eigenvalue problem

Guizhou Normal University（贵州师范大学）

本文讨论了凹多边形域上Steklov特征值问题的有限元近似，利用非配准Crouzeix-Raviart元的正则性估计和边平均插值算子特性，证明了新的最优误差估计，改进了现有结果，并通过数值实验验证。

2017-01-09cs.NAmath.NA

一个用于光滑平面域Steklov特征值问题的边界积分方程方法

A boundary integral equation method for Steklov eigenvalue problems for smooth planar domains

Wichita State University（威奇托州立大学）；Aalto University（阿尔托大学）；University of Turku（图尔库大学）

本文研究了通过谐 conjugation 的边界-only 方法对光滑单连通平面域的Steklov谱进行准确近似的计算问题，通过傅里叶差分和边界积分方程构建了稠密的代数特征值问题，展示了高精度和几何变化对Steklov谱的影响。

2026-10-19cs.NAmath.NA

一种用于表面微分算子本征值的无网格方法，包括斯蒂科夫问题

A Meshfree Method for Eigenvalues of Differential Operators on Surfaces, Including Steklov Problems

Simon Fraser University（西蒙菲莎大学）

本文提出了一种无网格方法，用于求解表面和平面域上微分算子的本征值问题，包括斯蒂科夫问题，并证明了高阶收敛性。

2025-06-16cs.NAmath.NA

Steklov eigenvalues for the Lamé operator in linear elasticity

In this paper we study Steklov eigenvalues for the Lamé operator which arise in the theory of linear elasticity. In this eigenproblem the spectral parameter appears in a Robin boundary condition, linking the traction and the displacement. To establish the existence of a countable spectrum for this problem, we present an extension of Korn's inequality. We also show that a proposed conforming Galerkin scheme provides convergent approximations to the true eigenvalues. A standard finite element method is used to conduct numerical experiments on 2D and 3D domains to support our theoretical findings…

2020-11-05cs.NAmath.APmath.NA

Approximation of the inverse scattering Steklov eigenvalues and the inverse spectral problem

In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been proposed to be used as a target signature since they can be recovered from the scattering data. A Galerkin method is studied where the basis functions are the Neumann eigenfunctions of the Laplacian. Error estimates for the eigenvalues and eigenfunctions are proven by appealing to Weyl's Law. We will test this method against separation of variables in order to …

2021-04-19cs.NAmath.APmath.NA

最小正则性下双调和Steklov特征值问题的协调与非协调虚拟元方法

Conforming and non-conforming virtual element methods for the biharmonic Steklov eigenvalue problem with minimum regularity

Indian Institute of Technology-Kharagpur（印度理工学院卡拉格普尔分校）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；Università di Pavia（帕维亚大学）；IMATI, Consiglio Nazionale delle Ricerche（国家研究委员会IMATI研究所）；Universidad Técnica Federico Santa María（费德里科·圣塔玛丽亚技术大学）

针对一般形状多边形域上的四阶Steklov特征值问题，提出协调和C^0非协调虚拟元方法，通过富化算子进行收敛分析，证明无伪特征值并得到最优收敛阶。

2026-06-16cs.NAmath.FAmath.NA