Volume 51, Issue 1
Numerical Assessment of a Class of High Order Stokes Spectrum Solver

Etienne Ahusborde, Mejdi Azaïez & Ralf Gruber

J. Math. Study, 51 (2018), pp. 1-14.

Published online: 2018-04

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  • Abstract

It is well known that the approximation of eigenvalues and associated eigenfunctions of a linear operator under constraint is a difficult problem. One of the difficulties is to propose methods of approximation which satisfy in a stable and accurate way the eigenvalues equations, the constraint one and the boundary conditions. Using any non-stable method leads to the presence of non-physical eigenvalues: a multiple zero one called spurious modes and non-zero one called pollution modes. One way to eliminate these two families is to favor the constraint equations by satisfying it exactly and to verify the equations of the eigenvalues equations in weak ways. To illustrate our contribution in this field we consider in this paper the case of Stokes operator. We describe several methods that produce the correct number of eigenvalues. We numerically prove how these methods are adequate to correctly solve the 2D Stokes eigenvalue problem.

  • AMS Subject Headings

76D07, 65N35, 34L16

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

etienne.ahusborde@univ-pau.fr (Etienne Ahusborde)

azaiez@enscbp.fr (Mejdi Azaïez)

ralf.gruber@bluewin.ch (Ralf Gruber)

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@Article{JMS-51-1, author = {Ahusborde , EtienneAzaïez , Mejdi and Gruber , Ralf}, title = {Numerical Assessment of a Class of High Order Stokes Spectrum Solver}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {51}, number = {1}, pages = {1--14}, abstract = {

It is well known that the approximation of eigenvalues and associated eigenfunctions of a linear operator under constraint is a difficult problem. One of the difficulties is to propose methods of approximation which satisfy in a stable and accurate way the eigenvalues equations, the constraint one and the boundary conditions. Using any non-stable method leads to the presence of non-physical eigenvalues: a multiple zero one called spurious modes and non-zero one called pollution modes. One way to eliminate these two families is to favor the constraint equations by satisfying it exactly and to verify the equations of the eigenvalues equations in weak ways. To illustrate our contribution in this field we consider in this paper the case of Stokes operator. We describe several methods that produce the correct number of eigenvalues. We numerically prove how these methods are adequate to correctly solve the 2D Stokes eigenvalue problem.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v51n1.18.01}, url = {http://global-sci.org/intro/article_detail/jms/11312.html} }
TY - JOUR T1 - Numerical Assessment of a Class of High Order Stokes Spectrum Solver AU - Ahusborde , Etienne AU - Azaïez , Mejdi AU - Gruber , Ralf JO - Journal of Mathematical Study VL - 1 SP - 1 EP - 14 PY - 2018 DA - 2018/04 SN - 51 DO - http://doi.org/10.4208/jms.v51n1.18.01 UR - https://global-sci.org/intro/article_detail/jms/11312.html KW - Stokes eigenvalues problem, spectral method. AB -

It is well known that the approximation of eigenvalues and associated eigenfunctions of a linear operator under constraint is a difficult problem. One of the difficulties is to propose methods of approximation which satisfy in a stable and accurate way the eigenvalues equations, the constraint one and the boundary conditions. Using any non-stable method leads to the presence of non-physical eigenvalues: a multiple zero one called spurious modes and non-zero one called pollution modes. One way to eliminate these two families is to favor the constraint equations by satisfying it exactly and to verify the equations of the eigenvalues equations in weak ways. To illustrate our contribution in this field we consider in this paper the case of Stokes operator. We describe several methods that produce the correct number of eigenvalues. We numerically prove how these methods are adequate to correctly solve the 2D Stokes eigenvalue problem.

Etienne Ahusborde, Mejdi Azaïez & Ralf Gruber. (2019). Numerical Assessment of a Class of High Order Stokes Spectrum Solver. Journal of Mathematical Study. 51 (1). 1-14. doi:10.4208/jms.v51n1.18.01
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