A Penalized Crouzeix–Raviart Element Method for Second Order Elliptic Eigenvalue Problems

Journal of Scientific Computing ◽

10.1007/s10915-017-0505-9 ◽

2017 ◽

Vol 74 (3) ◽

pp. 1457-1479

Author(s):

Jun Hu ◽

Limin Ma

Keyword(s):

Eigenvalue Problems ◽

Second Order ◽

Elliptic Eigenvalue Problems ◽

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Virtual element method for second-order elliptic eigenvalue problems

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drx063 ◽

2017 ◽

Vol 38 (4) ◽

pp. 2026-2054 ◽

Author(s):

Francesca Gardini ◽

Giuseppe Vacca

Keyword(s):

Eigenvalue Problems ◽

Second Order ◽

Virtual Element Method ◽

Virtual Element ◽

Elliptic Eigenvalue Problems ◽

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On a finite element method for second order elliptic eigenvalue problems with nonlocal direchlet boundary conditions

Numerical Functional Analysis and Optimization ◽

10.1080/01630569708816760 ◽

1997 ◽

Vol 18 (3-4) ◽

pp. 283-295 ◽

Author(s):

H. De Schepper ◽

R. Van Keer

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Boundary Conditions ◽

Eigenvalue Problems ◽

Second Order ◽

Elliptic Eigenvalue Problems ◽

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Least squares h-p spectral element method for elliptic eigenvalue problems

Applied Mathematics and Computation ◽

10.1016/j.amc.2012.01.078 ◽

2012 ◽

Vol 218 (19) ◽

pp. 9596-9613 ◽

Author(s):

Lokendra K. Balyan ◽

Pravir K. Dutt ◽

R.K.S. Rathore

Keyword(s):

Least Squares ◽

Spectral Element Method ◽

Eigenvalue Problems ◽

Spectral Element ◽

Elliptic Eigenvalue Problems ◽

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A Numerical Method Based on Higher Order Polynomial Approximation for Second Order Elliptic Eigenvalue Problems on Arbitrary Convex Quadrilateral Domain

Advances in Applied Mathematics ◽

10.12677/aam.2021.1012446 ◽

2021 ◽

Vol 10 (12) ◽

pp. 4201-4208

Author(s):

继会郑

Keyword(s):

Numerical Method ◽

Polynomial Approximation ◽

Eigenvalue Problems ◽

Higher Order ◽

Second Order ◽

Convex Quadrilateral ◽

Order Polynomial ◽

Arbitrary Convex ◽

Elliptic Eigenvalue Problems

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A finite element method for elliptic eigenvalue problems in a multi-component domain in 2D with non-local Dirichlet transition conditions

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(99)00147-8 ◽

1999 ◽

Vol 111 (1-2) ◽

pp. 253-265 ◽

Author(s):

Hennie De Schepper ◽

Roger Van Keer

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Eigenvalue Problems ◽

Non Local ◽

Elliptic Eigenvalue Problems ◽

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Error estimates of the quadrature finite element method with biquadratic finite elements for elliptic eigenvalue problems in the square domain

Journal of Physics Conference Series ◽

10.1088/1742-6596/1158/4/042021 ◽

2019 ◽

Vol 1158 ◽

pp. 042021

Author(s):

S I Solov’ev ◽

P S Solov’ev

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Finite Elements ◽

Error Estimates ◽

Eigenvalue Problems ◽

Elliptic Eigenvalue Problems ◽

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Classification of second-order linear differential equations and an application to singular elliptic eigenvalue problems

Bulletin of the London Mathematical Society ◽

10.1112/blms/bdr117 ◽

2012 ◽

Vol 44 (3) ◽

pp. 545-562 ◽

Author(s):

Yūki Naito

Keyword(s):

Differential Equations ◽

Eigenvalue Problems ◽

Second Order ◽

Linear Differential Equations ◽

Order Linear ◽

Linear Differential ◽

Elliptic Eigenvalue Problems

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An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/1995290303391 ◽

1995 ◽

Vol 29 (3) ◽

pp. 339-365 ◽

Author(s):

M. Vanmaele ◽

R. Van Keer

Keyword(s):

Finite Element ◽

Composite Structures ◽

Eigenvalue Problems ◽

Operator Method ◽

Finite Element Approximation ◽

Second Order ◽

Numerical Quadrature ◽

Element Approximation ◽

Elliptic Eigenvalue Problems

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Quadrature finite element method for elliptic eigenvalue problems

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080217050341 ◽

2017 ◽

Vol 38 (5) ◽

pp. 856-863 ◽

Author(s):

S. I. Solov’ev

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Eigenvalue Problems ◽

Elliptic Eigenvalue Problems ◽

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CONVERGENCE OF ADAPTIVE FINITE ELEMENT METHODS FOR EIGENVALUE PROBLEMS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202509003590 ◽

2009 ◽

Vol 19 (05) ◽

pp. 721-747 ◽

Author(s):

EDUARDO M. GARAU ◽

PEDRO MORIN ◽

CARLOS ZUPPA

Keyword(s):

Finite Element ◽

Finite Elements ◽

Finite Element Methods ◽

Eigenvalue Problems ◽

Second Order ◽

Adaptive Finite Element ◽

Adaptive Finite Element Methods ◽

Multiple Eigenvalues ◽

Elliptic Eigenvalue Problems

In this paper we prove convergence of adaptive finite element methods for second-order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.

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