Journal ArticleDOI
Comparison of some finite element methods for solving the diffusion-convection-reaction equation
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TLDR
It is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerskin method has a stabilization effect similar to a sub-grid scale model, which is in turn related to the introduction of bubble functions.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1998-04-14. It has received 482 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.read more
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Journal ArticleDOI
Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
TL;DR: In this paper, a stabilized finite element method is proposed to solve the transient Navier-Stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales.
Journal ArticleDOI
On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I – A review
Volker John,Petr Knobloch +1 more
TL;DR: A review and state of the art of these methods can be found in this article, which discusses their derivation, proposes some alternative choices of parameters in the methods and categorizes them.
Journal ArticleDOI
A stabilized finite element method for generalized stationary incompressible flows
TL;DR: A finite element formulation for the numerical solution of the stationary incompressible Navier–Stokes equations including Coriolis forces and the permeability of the medium using the algebraic version of the sub-grid scale approach.
Journal ArticleDOI
Stabilization of Galerkin approximations of transport equations by subgrid modeling
TL;DR: In this paper, an artificial diffusion based on a two-level decomposition of the approximation space is proposed for approximating transport equations, which is proved to have stability and convergence properties that are similar to that of the streamline diffusion method.
Reference EntryDOI
Multiscale and Stabilized Methods
TL;DR: A general treatment of the variational multiscale method in the context of an abstract Dirichlet problem is then presented which is applicable to advective-diffusive processes and other processes of physical interest as mentioned in this paper.
References
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Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Journal ArticleDOI
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more
TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.
Book
Mixed and Hybrid Finite Element Methods
Franco Brezzi,Michel Fortin +1 more
TL;DR: Variational Formulations and Finite Element Methods for Elliptic Problems, Incompressible Materials and Flow Problems, and Other Applications.
Book
Numerical methods for conservation laws
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
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Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more