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Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2009年第1期358卷 136-147页

作者： Efendiev, Messoud Nakaguchi, Etsushi Wendland, Wolfgang L. Univ Stuttgart Dept Math D-70550 Stuttgart Germany Tech Univ Munich Dept Math D-85747 Garching Germany Tokyo Med & Dent Univ Coll Liberal Arts & Sci Chiba 2720827 Japan

In this paper we continue systematic study of the dimension estimate of the global attractors for the chemotaxis-growth system and its finite-element approximations. Utilizing a conservative upwind finite-element scheme we managed significantly to improve dimension estimates with respect to the chemotactic parameter. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Dimension of global attractor finite-element approximation Upwind scheme Nonnegativity of solution Chemotaxis-growth system

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A finite-element approximation of a quasi-magnetostatic 3D eddy current model by fractional-step A-ψ scheme

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MATHEMATICAL AND COMPUTER MODELLING 2004年第4-5期39卷 567-580页

作者： Ma, CF Guilin Inst Elect Technol Dept Computat Sci & Appl Phys Guilin 541004 Peoples R China

We propose in this paper a fractional-step A-psi scheme for a quasi-magnetostatic 3D eddy current model by means of finite-element approximations. Bounds for continuous and discrete error in finite time are given, and it is verified that provided the time step tau is sufficiently small, the proposed algorithm yields for finite time T an error of O(rooth(2) + tau(2)) in the L-2-norm for the magnetic field H(= vdel x A), where h is the mesh size. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： eddy current problem fractional-step A-psi scheme finite-element approximation error estimates

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Asymptotic exactness of an a posteriori error estimator based on the equilibrated residual method

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NUMERISCHE MATHEMATIK 2007年第2期106卷 225-253页

作者： Maxim, Andrei Cornell Univ Dept Math Ithaca NY 14853 USA

In this paper we analyze an a posteriori error estimator based on the equilibrated residual method. We prove that this estimator is asymptotically exact in the energy norm for regular solutions and O(h(1+alpha)) (alph... 详细信息

关键词： finite-element approximation

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Error estimates of finite-element approximations for a fourth-order differential equation

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2006年第3-4期52卷 283-288页

作者： Ohm, M. R. Lee, H. Y. Shin, J. Y. Pukyong Natl Univ Div Math Sci Pusan 608737 South Korea Dongseo Univ Div Informat Syst Engn Pusan 617716 South Korea Kyungsung Univ Dept Math Pusan 608736 South Korea

finite-element approximations for a fourth-order differential equation based on the space of piecewise linear polynomials on the uniform grid are introduced. And error estimates for the approximation are also given. (... 详细信息

关键词： hinged beam fourth-order differential equation finite-element approximation error estimates

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Error bounds for the finite-element approximation of the exterior Stokes equations in two dimensions

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IMA JOURNAL OF NUMERICAL ANALYSIS 2003年第1期23卷 125-148页

作者： Bao, WZ Natl Univ Singapore Dept Computat Sci Singapore 117543 Singapore

In this paper we design high-order (non)local artificial boundary conditions (ABCs) which are different from those proposed by Han, H. & Bao, W. (1997 Numer. Math., 77, 347-363) for incompressible materials, and present error bounds for the finite-element approximation of the exterior Stokes equations in two dimensions. The finite-element approximation (especially its corresponding stiff matrix) becomes much simpler (sparser) when it is formulated in a bounded computational domain using the new (non)local approximate ABCs. Our error bounds indicate how the errors of the finite-element approximations depend on the mesh size, terms used in the approximate ABCs and the location of the artificial boundary. Numerical examples of the exterior Stokes equations outside a circle in the plane are presented. Numerical results demonstrate the performance of our error bounds.

关键词： exterior Stokes equations finite-element approximation artificial boundary (non)local artificial boundary condition (ABC) error bounds

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Wall-driven incompressible viscous flow in a two-dimensional semi-circular cavity

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JOURNAL OF COMPUTATIONAL PHYSICS 2006年第1期216卷 76-91页

作者： Glowinski, R. Guidoboni, G. Pan, T. -W. Univ Houston Dept Math Houston TX 77204 USA Univ Paris 06 Lab Jacques Louis Lions F-75005 Paris France Univ Ferrara Dipartmento Matemat I-44100 Ferrara Italy

The main goal of this article is to investigate the capability of an operator-splitting/finite elements based methodology at handling accurately incompressible viscous flow at large Reynolds number (Re) in regions with corners and curved boundaries. To achieve this goal the authors have selected a wall-driven flow in a semi-circular cavity. On the basis of the numerical experiments reported in this article it seems that the method under investigation has no difficulty at capturing the formation of primary, secondary and tertiary vortices as Re increases;it has also the capability of identifying a Hopf bifurcation phenomenon taking place around Re = 6600. (c) 2005 Elsevier Inc. All rights reserved.

关键词： finite-element approximation NAVIER-STOKES EQUATIONS STABILITY

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Variational models for moving contact lines and the quasi-static approximation

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EUROPEAN JOURNAL OF APPLIED MATHEMATICS 2005年第6期16卷 713-740页

作者： Glasner, K. B. Univ Arizona Dept Math Tucson AZ 85721 USA

This paper proposes the use of a variational framework to model fluid wetting dynamics. The central problem of infinite energy dissipation for a moving contact line is dealt with explicitly rather than by introducing a specific microscopic mechanism which removes it. We analyze this modelling approach in the context of the quasi-steady limit, where contact line motion is slower than bulk relaxation. We find that global effects enter into Tanner-type laws which relate line velocity to apparent contact angle through the role that energy dissipation plays in the bulk of the fluid. A comparison is made to the dynamics of lubrication equations that include attractive and repulsive intermolecular interactions. A Galerkin-type approximation method is introduced which leads to reduced-dimensional dynamical descriptions. Computations are conducted using these low-dimensional approximations, and a substantial connection to lubrication equation dynamics is found.

关键词： CAHN-HILLIARD EQUATION finite-element approximation THIN VISCOUS FILMS SOLID-SURFACE FLUID INTERFACE LUBRICATION approximation DEGENERATE MOBILITY PATTERN-FORMATION FREE-ENERGY DYNAMICS CAHN-HILLIARD EQUATION solid surfaces Free energy dynamics Energy dissipation MOVING CONTACTS contact angle finite element approximation method Lubrication CONTACT LINE

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Limit analysis method in elastostatics and electrostatics

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2005年第3期28卷 253-273页

作者： Brigadnov, IA NW State Tech Univ Dept Comp Sci St Petersburg 191186 Russia

The limit analysis method for an estimation of mechanical and electrical strength safety conditions for non-linear elastic and dielectric solids, respectively, is examined. By the variational method and the duality theory, the appropriate initial and dual limit analysis problems (LAPs) are formulated. It is demonstrated that the initial LAPs need a relaxation, but the appropriate fully relaxed problems have no clear physical interpretation. On the other hand, the dual LAPs have a clear physical interpretation. The general initial and dual LAPs for quasi-static problems of Continuum Mechanics are formulated. The appropriate 2-D finite-element approximations and numerical solutions are presented. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： limit analysis method non-linear elasticity electrostatics variational method duality theory finite-element approximation numerical methods

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Semidiscretization and error estimates for distributed control of the instationary Navier-Stokes equations

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NUMERISCHE MATHEMATIK 2004年第2期97卷 297-320页

作者： Deckelnick, K Hinze, M Tech Univ Dresden Fak Math Inst Numer Math D-01062 Dresden Germany Univ Magdeburg Inst Anal & Numer D-39106 Magdeburg Germany

Optimal control problems governed by the two-dimensional instationary Navier-Stokes equations and their spatial discretizations with finite elements are investigated. A concept of semi-discrete solutions to the control problem is introduced which is utilized to prove existence and uniqueness of discrete controls in neighborhoods of regular continuous solutions. Furthermore, an optimal error estimate in terms of the spatial discretization parameter is given.

关键词： finite-element approximation VELOCITY TRACKING PROBLEM SPATIALDISCRETIZATION BOUNDARY CONTROL TIME FLOWS

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Asymptotic behavior and time discretization analysis for the non-stationary Navier-Stokes problem

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NUMERISCHE MATHEMATIK 2004年第4期98卷 647-673页

作者： He, YN Li, KT Xian Jiaotong Univ Fac Sci State Key Lab Multiphase Flow Power Engn Xian 710049 Peoples R China

The asymptotic behavior and the Euler time discretization analysis are presented for the two-dimensional non-stationary Navier-Stokes problem. If the data nu and lim f(t) satisfy a uniqueness condition corresponding to the stationary Navier-Stokes problem, we then obtain the convergence of the non-stationary Navier-Stokes problem to the stationary Navier-Stokes problem and the uniform boundedness, stability and error estimates of the Euler time discretization for the non-stationary Navier-Stokes problem.

关键词： finite-element approximation CONVERGENCE REGULARITY EQUATIONS STABILITY UNIFORM

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