Abstract
We present in this paper a stable spectral element for the approximations of the grad(div) eigenvalue problem in two and three-dimensional quadrangular geometry. Spectral approximations based on Gaussian quadrature rules are built in a dual variational approach with Darcy type equations. We prove that spectral convergence can be reached for the irrotational spectrum without the presence of any spurious eigenmodes, provided an adequate choice is made for the quadrature rules.
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Azaïez, M., Gruber, R., Deville, M.O. et al. On a Stable Spectral Method for the grad(div) Eigenvalue Problem. J Sci Comput 27, 41–50 (2006). https://doi.org/10.1007/s10915-005-9037-9
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DOI: https://doi.org/10.1007/s10915-005-9037-9