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A note about nonconforming finite element approximations of the Steklov eigenvalue problem. (Chinese. English summary) Zbl 1212.65435

Summary: This paper explores nonconforming finite element approximations of the Steklov eigenvalue problem where \(\varOmega\) is a bounded concave polygonal domain. Numerical results show that the approximate eigenvalues derived from the nonconforming Crouzeix-Raviart element, the \(Q^{\mathrm{rot}}_1\) element and the \(EQ^{\mathrm{rot}}_1\) element have the same convergence order as that obtained from the piecewise linear conforming finite element and provide lower bounds for the exact eigenvalues.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
65N15 Error bounds for boundary value problems involving PDEs
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