The extrapolation of numerical eigenvalues by finite elements for differential operators |
| |
Institution: | 1. Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China;2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland |
| |
Abstract: | This paper discusses the extrapolation of numerical eigenvalues by finite elements for differential operators and obtains the following new results: (a) By extending a theorem of eigenvalue error estimate, which was established by Osborn, a new expansion of eigenvalue error is obtained. Many achievements, which are about the asymptotic expansions of finite element methods of differential operator eigenvalue problems, are brought into the framework of functional analysis. (b) The Richardson extrapolation of nonconforming finite elements for multiple eigenvalues and splitting extrapolation of finite elements based on domain decomposition of non-selfadjoint differential operators for multiple eigenvalues are achieved. In addition, numerical examples are provided to support the theoretical analysis. |
| |
Keywords: | Spectral approximation Multiple eigenvalue Finite element Asymptotic expansion Splitting extrapolation |
本文献已被 ScienceDirect 等数据库收录! |
|