Lower spectral bounds by Wilson's brick discretization

• Autores: Yidu Yang, Hai Bi
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 8, 2010, págs. 782-787
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.03.019
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• Resumen

  • This paper discusses the Wilson element approximation for the eigenvalue problem of Laplace operator on n-dimensional polygonal domain (n=2,3), and the main results are as follows: (1) We establish the relationship between the interpolation weak estimate of the Wilson element and the interpolation weak estimate of n-linear element. (2) We prove that 3-dimensional Wilson's brick eigenvalues approximate the exact eigenvalues from below, and thereby make a new progress on such an open problem in the finite element method.