Generalized Rayleigh quotient and finite element two-grid discretization schemes
This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) The Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of the exact eigenvalue with the ascent of the finite element approximate eigenvalue. 3) Based on the work of \textit{J. Xu} and \textit{A. Zhou} [Math. Comput. 70, No. 233, 17--25 (2001; Zbl 0959.65119)], finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and nonconforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
nonselfadjoint elliptic eigenvalue problem
scientific article; zbMATH DE number 5645737
scientific article