Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
New expansions of numerical eigenvalues by Wilson's element
Journal of Computational and Applied Mathematics
Nonconforming finite element approximations of the Steklov eigenvalue problem
Applied Numerical Mathematics
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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.