$hp$-Finite Elements for Elliptic Eigenvalue Problems: Error Estimates Which Are Explicit with Respect to $\lambda$, h, and p

S. Sauter

doi:10.1137/070702515

$hp$-Finite Elements for Elliptic Eigenvalue Problems: Error Estimates Which Are Explicit with Respect to $\lambda$, h, and p

SIAM Journal on Numerical Analysis ◽

10.1137/070702515 ◽

2010 ◽

Vol 48 (1) ◽

pp. 95-108 ◽

Cited By ~ 15

Author(s):

S. Sauter

Keyword(s):

Finite Elements ◽

Error Estimates ◽

Eigenvalue Problems ◽

Hp Finite Elements ◽

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 ◽

Element Method

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A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques

Journal of Scientific Computing ◽

10.1007/s10915-021-01572-2 ◽

2021 ◽

Vol 88 (3) ◽

Author(s):

Stefano Giani ◽

Luka Grubišić ◽

Harri Hakula ◽

Jeffrey S. Ovall

Keyword(s):

Error Estimates ◽

Eigenvalue Problems ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Elliptic Eigenvalue Problems

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Essentially optimal finite elements for multiscale elliptic eigenvalue problems

Advances in Computational Mathematics ◽

10.1007/s10444-021-09903-5 ◽

2021 ◽

Vol 47 (6) ◽

Author(s):

Pham Quy Muoi ◽

Wee Chin Tan ◽

Viet Ha Hoang

Keyword(s):

Finite Elements ◽

Eigenvalue Problems ◽

Elliptic Eigenvalue Problems

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A note on the residual type a posteriori error estimates for finite element eigenpairs of nonsymmetric elliptic eigenvalue problems

Applied Numerical Mathematics ◽

10.1016/j.apnum.2014.02.015 ◽

2014 ◽

Vol 82 ◽

pp. 51-67 ◽

Cited By ~ 4

Author(s):

Yidu Yang ◽

Lingling Sun ◽

Hai Bi ◽

Hao Li

Keyword(s):

Finite Element ◽

Error Estimates ◽

Eigenvalue Problems ◽

A Posteriori Error Estimates ◽

Type A ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Elliptic Eigenvalue Problems

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Local a priori/a posteriori error estimates of conforming finite elements approximation for Steklov eigenvalue problems

Science China Mathematics ◽

10.1007/s11425-013-4709-7 ◽

2013 ◽

Vol 57 (6) ◽

pp. 1319-1329 ◽

Cited By ~ 7

Author(s):

YiDu Yang ◽

Hai Bi

Keyword(s):

Finite Elements ◽

Error Estimates ◽

Eigenvalue Problems ◽

A Priori ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Steklov Eigenvalue ◽

Steklov 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 ◽

Cited By ~ 32

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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