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A real-valued block conjugate gradient type method for solving complex symmetric linear systems with multiple right-hand sides

Yasunori Futamura, Takahiro Yano, Akira Imakura, Tetsuya Sakurai (2017)

Applications of Mathematics

We consider solving complex symmetric linear systems with multiple right-hand sides. We assume that the coefficient matrix has indefinite real part and positive definite imaginary part. We propose a new block conjugate gradient type method based on the Schur complement of a certain 2-by-2 real block form. The algorithm of the proposed method consists of building blocks that involve only real arithmetic with real symmetric matrices of the original size. We also present the convergence property of...

A Recession Notion for a Class of Monotone Bivariate Functions

Moudafi, A. (2000)

Serdica Mathematical Journal

Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.

A recovery-based a posteriori error estimator for the generalized Stokes problem

Pengzhan Huang, Qiuyu Zhang (2020)

Applications of Mathematics

A recovery-based a posteriori error estimator for the generalized Stokes problem is established based on the stabilized P 1 - P 0 (linear/constant) finite element method. The reliability and efficiency of the error estimator are shown. Through theoretical analysis and numerical tests, it is revealed that the estimator is useful and efficient for the generalized Stokes problem.

A reduced basis element method for the steady Stokes problem

Alf Emil Løvgren, Yvon Maday, Einar M. Rønquist (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations. The method takes its roots in domain decomposition methods and reduced basis discretizations. The basic idea is to first decompose the computational domain into a series of subdomains that are deformations of a few reference domains (or generic computational parts). Associated with each reference domain are precomputed solutions corresponding to the same...

A Reduced Basis Enrichment for the eXtended Finite Element Method

E. Chahine, P. Laborde, Y. Renard (2009)

Mathematical Modelling of Natural Phenomena

This paper is devoted to the introduction of a new variant of the extended finite element method (Xfem) for the approximation of elastostatic fracture problems. This variant consists in a reduced basis strategy for the definition of the crack tip enrichment. It is particularly adapted when the asymptotic crack-tip displacement is complex or even unknown. We give a mathematical result of quasi-optimal a priori error estimate and some computational tests including a comparison with some other strategies....

A reduced model for Darcy’s problem in networks of fractures

Luca Formaggia, Alessio Fumagalli, Anna Scotti, Paolo Ruffo (2014)

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

Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures...

A refined Newton’s mesh independence principle for a class of optimal shape design problems

Ioannis Argyros (2006)

Open Mathematics

Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.

A remark about a Galerkin method

Gerhard Ströhmer (1996)

Banach Center Publications

It is shown that the approximating equations whose existence is required in the author's previous work on partially regular weak solutions can be constructed without any additional assumption about the equation itself. This leads to a variation of a Galerkin method.

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