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A full multigrid method for semilinear elliptic equation

Fei Xu, Hehu Xie (2017)

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 proof of monotony of the Temple quotients in eigenvalue problems

Karel Rektorys (1984)

Aplikace matematiky

If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue λ 1 , the sequences of the so-called Schwarz quatients (which are upper bounds for λ 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 Superconvergence result for mixed finite element approximations of the eigenvalue problem

Qun Lin, Hehu Xie (2012)

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∗

Qun Lin, Hehu Xie (2012)

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...

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