Mixed approximation of eigenvalue problems: A superconvergence result

Francesca Gardini

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 5, page 853-865
  • ISSN: 0764-583X

Abstract

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We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini approximation.

How to cite

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Gardini, Francesca. "Mixed approximation of eigenvalue problems: A superconvergence result." ESAIM: Mathematical Modelling and Numerical Analysis 43.5 (2009): 853-865. <http://eudml.org/doc/250592>.

@article{Gardini2009,
abstract = { We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini approximation. },
author = {Gardini, Francesca},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Eigenvalue problem; mixed finite element; superconvergence result; eigenvalue problem; mixed finite element method; superconvergence; Laplace problem; Poisson equation; Raviart-Thomas approximation; Neumann boundary condition; Crouzeix-Raviart approximation; numerical experiments},
language = {eng},
month = {4},
number = {5},
pages = {853-865},
publisher = {EDP Sciences},
title = {Mixed approximation of eigenvalue problems: A superconvergence result},
url = {http://eudml.org/doc/250592},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Gardini, Francesca
TI - Mixed approximation of eigenvalue problems: A superconvergence result
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/4//
PB - EDP Sciences
VL - 43
IS - 5
SP - 853
EP - 865
AB - We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini approximation.
LA - eng
KW - Eigenvalue problem; mixed finite element; superconvergence result; eigenvalue problem; mixed finite element method; superconvergence; Laplace problem; Poisson equation; Raviart-Thomas approximation; Neumann boundary condition; Crouzeix-Raviart approximation; numerical experiments
UR - http://eudml.org/doc/250592
ER -

References

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  12. F. Gardini, A posteriori error estimates for eigenvalue problems in mixed form. Ist. lombardo Accd. Sci. Lett. Rend. A.138 (2004) 17–34.  Zbl1203.76114
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  14. F. Gardini, A posteriori error estimates for eigenvalue problems in mixed form. Ph.D. Thesis, Università degli Studi di Pavia, Pavia, Italy (2005).  Zbl1277.65090
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