Journal ArticleDOI
On stabilized finite element methods for linear systems of convection-diffusion-reaction equations
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TLDR
In this article, a stabilized finite element method for solving convection-diffusion-reaction equations is studied, which is based on the subgrid scale approach and an algebraic approximation to the subscales.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2000-07-21. It has received 192 citations till now. The article focuses on the topics: Finite element method & Stiffness matrix.read more
Citations
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Journal ArticleDOI
Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods
TL;DR: Two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the Stokes problem are analyzed and it is shown here that the first method can also be recast in the framework of sub-grid scale methods with a particular choice for the space ofSub-scales.
Journal ArticleDOI
Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes
TL;DR: In this article, the authors combine NURBS-based isogeometric analysis, residual-driven turbulence modeling and weak imposition of no-slip and no-penetration Dirichlet boundary conditions on unstretched meshes to compute wall-bounded turbulent flows.
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.
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.
Journal ArticleDOI
On Finite Element Methods for 3D Time-Dependent Convection-Diffusion-Reaction Equations with Small Diffusion
Volker John,Ellen Schmeyer +1 more
TL;DR: In this article, the SUPG method, a SOLD method and two types of FEM-FCT methods are compared with a 3D example with nonhomogeneous Dirichlet boundary conditions and homogeneous Neumann boundary conditions.
References
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Book
The Mathematical Theory of Finite Element Methods
TL;DR: In this article, the construction of a finite element of space in Sobolev spaces has been studied in the context of operator-interpolation theory in n-dimensional variational problems.
Journal ArticleDOI
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.
Journal ArticleDOI
A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations
TL;DR: Galerkin/least-squares finite element methods for advective-diffusive equations are presented in this paper, and a convergence analysis and error estimates are presented.
Journal ArticleDOI
Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements
TL;DR: In this paper, a finite element formulation based on stabilized bilinear and linear equal-order-interpolation velocity-pressure elements is presented for computation of steady and unsteady incompressible flows.
Journal ArticleDOI
Stabilized finite element methods. II: The incompressible Navier-Stokes equations
Leopoldo P. Franca,Sérgio Frey +1 more
TL;DR: Stabilized methods are proposed and analyzed for a linearized form of the incompressible Navier-Stokes equations, allowing any combination of velocity and continuous pressure interpolations and generalizing previous works restricted to low-order interpolations.
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