Journal Article10.1016/J.CMA.2009.11.023
Consistent SUPG-method for transient transport problems: Stability and convergence
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TL;DR: In this article, the authors considered the time/space discretization of the transient advection equation and proved uniform stability of the general formulation under a regularity condition on data, or a moderate inverse CFL-condition that allows for optimal choices of the discretisation parameters.
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About: This article is published in Computer Methods in Applied Mechanics and Engineering. The article was published on 01 Mar 2010. The article focuses on the topics: Backward Euler method & Upwind scheme.
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Citations
Robust Numerical Methods for Singularly Perturbed Differential Equations: A Survey Covering 2008–2012
TL;DR: In this article, the authors present new results in numerical analysis of singularly perturbed convection-diffusion-reaction problems that have appeared in the last five years, mainly discussing layer-adapted meshes.
Error Analysis of the SUPG Finite Element Discretization of Evolutionary Convection-Diffusion-Reaction Equations
Volker John,Julia Novo +1 more
TL;DR: The main focus of the paper consists in deriving estimates in which the stabilization parameters do not depend on the length of the time step, and it is shown that such estimates can be obtained in the case of time-independent convection and reaction.
118
Order preserving SUPG stabilization for the Virtual Element formulation of advection-diffusion problems
TL;DR: Numerical results clearly show the stabilizing effect of the Virtual Element Method up to very large Peclet numbers and are in very good agreement with the expected rate of convergence.
116
Upwind residual discretization of enhanced Boussinesq equations for wave propagation over complex bathymetries
TL;DR: In this paper, the authors investigated the applicability of upwind and stabilized variants of continuous Galerkin finite element and residual distribution schemes for the simulation of wave propagation and transformation over complex bathymetries.
72
References
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.
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Galerkin Finite Element Methods for Parabolic Problems
Vidar Thomée
- 01 Jun 1984
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
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Finite-element approximations of the nonstationary Navier-Stokes problem. Part IV: error estimates for second-order time discretization
John G. Heywood,Rolf Rannacher +1 more
TL;DR: This paper provides an error analysis for the Crank–Nicolson method of time discretization applied to spatially discrete Galerkin approximations of the nonstationary Navier–Stokes equations.
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Finite element methods for linear hyperbolic problems
TL;DR: A survey of finite element methods for convectiondiffusion problems and first-order linear hyperbolic problems can be found in this article, where the authors give a survey of some recent work by the authors.
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