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
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TLDR
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.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1990-09-01. It has received 5157 citations till now. The article focuses on the topics: Upwind scheme & Streamline diffusion.read more
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Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement
TL;DR: In this article, the concept of isogeometric analysis is proposed and the basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model.
Journal ArticleDOI
Reproducing kernel particle methods
TL;DR: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed and is called the reproducingkernel particle method (RKPM).
Book
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
TL;DR: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software.
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TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: In this paper, a classe de methodes a elements finis de Galerkin discontinues a variation totale bornee for the resolution des lois de conservation, and the convergence of the convergence is studied.
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Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
TL;DR: In this paper, an approach is developed for deriving variational methods capable of representing multiscale phenomena, which leads to the well-known Dirichlet-to-Neumann formulation.
References
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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
Numerical solution of the Navier-Stokes equations
TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
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An ‘upwind’ finite element scheme for two‐dimensional convective transport equation
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Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation
TL;DR: In this article, a review of recent work and new developments for the penalty function/finite element formulation of incompressible viscous flows is presented, in the context of the steady and unsteady Navier-Stokes equations.
Journal ArticleDOI
Finite element methods for second order differential equations with significant first derivatives
TL;DR: Asymmetric linear and quadratic basis functions are introduced and shown to overcome the difficulty ofGalerkin finite element methods in an appropriate two point boundary value problem.