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### A full multigrid method for semilinear elliptic equation

Applications of Mathematics

A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as...

### A multilevel Newton's method for eigenvalue problems

Applications of Mathematics

We propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue...

### A proof of monotony of the Temple quotients in eigenvalue problems

Aplikace matematiky

If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue ${\lambda }_{1}$, the sequences of the so-called Schwarz quatients (which are upper bounds for ${\lambda }_{1}$) and of the so-called Temple quotients (which are lower bounds) are constructed. While monotony of the first sequence was proved many years ago, monotony of the second one has been proved only recently by F. goerisch and J. Albrecht in their common paper “Die Monotonie der Templeschen Quotienten” (ZAMM, in print). In the present...

### A simple proof of the spectral continuity of the Sturm-Liouville problem

Banach Center Publications

### A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-finite domain.

Numerische Mathematik

### A Superconvergence result for mixed finite element approximations of the eigenvalue problem

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic...

### A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic...

### Accurate computation of higher Sturm-Liouville eigenvalues.

Numerische Mathematik

### An a posteriori Error Estimation of the Rayleigh-Ritz Eigenvalues.

Numerische Mathematik

### An Iteration Method for Studying the Bifurcation of Solutions of the Nonlinear Equations, L(...) u + ..R (..., u) = 0 .

Numerische Mathematik

### Analysis and comparison of several components mode synthesis methods on one-dimensional domains.

Numerische Mathematik

### Application of the direct method to a microconvection model.

Acta Universitatis Apulensis. Mathematics - Informatics

### Approximation of eigenvalues of differential equations with non-smooth coefficients

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

### Beziehungen zwischen den Verfahren von Ritz und Bazley

Acta Universitatis Carolinae. Mathematica et Physica

### Branch Switching in Bifurcation Problems for Ordinary Differential Equations

Numerische Mathematik

### Chord Techniques and Newton's Method for Discrete Bifurcation Problems.

Numerische Mathematik

### Comparison between the variational iteration method and the homotopy perturbation method for the Sturm-Liouville differential equation.

Boundary Value Problems [electronic only]

### Correction of Finite Element Estimates for Sturm-Liouville Eigenvalues.

Numerische Mathematik

### Correction of Numerov's Eigenvalue Estimates.

Numerische Mathematik

### Discrete Inverse Sturm-Liouville Problems. I. Uniqueness for Symmetric Potentials.

Numerische Mathematik

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