A challenging test for convergence accelerators: summation of a series with a special sign pattern.
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Sidi, Avram (2006)
Applied Mathematics E-Notes [electronic only]
Bailey, David H., Jeyabalan, Karthik, Li, Xiaoye S. (2005)
Experimental Mathematics
Guido Walz (1987)
Numerische Mathematik
J.B. Kioustelidis (1979)
Numerische Mathematik
Qun Lin, Shu Hua Zhang (1997)
Applications of Mathematics
In this paper we study the finite element approximations to the Sobolev and viscoelasticity type equations and present a direct analysis for global superconvergence for these problems, without using Ritz projection or its modified forms.
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...
C. Brezinski (1980)
Numerische Mathematik
Ren, Hongmin, Yang, Shijun (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Roberto Barrio (1998)
Extracta Mathematicae
W. Hackbusch, S. Dittrich (1980)
Numerische Mathematik
Yunhui He, Yu Li, Hehu Xie, Chun'guang You, Ning Zhang (2018)
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...
Roland Ernst, Bernd Flemisch, Barbara Wohlmuth (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.
Xiaohui Hu, Pengzhan Huang, Xinlong Feng (2016)
Applications of Mathematics
In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers’ equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.
L. WUYTACK (1971)
Numerische Mathematik
H. I. Miller (1973)
Matematički Vesnik
D.A. Field, W.B. Jones (1972)
Numerische Mathematik
Jaroslav Markl (1983)
Kybernetika
O. Awono, J. Tagoudjeu (2010)
Mathematical Modelling of Natural Phenomena
We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...
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...
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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