Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method
The paper is concerned with symmetric Neumann eigenvalue problems for second-order elliptic differential operators. The problem is formulated as a saddle-point problem, and a mixed finite element scheme is considered for its numerical solution. The eigenvalue error is represented in terms of the exact solution and its finite element interpolant. Based on this representation, an asymptotic expansion of the eigenvalue error is obtained, which is used to derive an extrapolation scheme. Three numerical examples, one of them on an \(L\)-shaped domain, are presented to illustrate the results.
second order elliptic eigenvalue problem
scientific article; zbMATH DE number 5574504
scientific article