Year: 2009
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 615–626
Abstract
We study the $n$-simplex nonconforming Crouzeix-Raviart element in approximating the $n$-dimensional second-order elliptic boundary value problems and the associated eigenvalue problems. By using the second Strang Lemma, optimal rate of convergence is established under the discrete energy norm. The error bound is also valid for the eigenfunction approximations. In addition, when eigenfunctions are singular, we prove that the Crouzeix-Raviart element approximates exact eigenvalues from below. Moreover, our numerical experiments demonstrate that the lower bound property is also valid for smooth eigenfunctions, although a theoretical justification is lacking.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-IJNAM-787
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 615–626
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: $n$-simplex nonconforming Crouzeix-Raviart element second order elliptic equation error estimates eigenvalues lower bound.