Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms
This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
Finite Element Approximation of the Navier-Stokes Equations
A mixed finite element method for solving the stokes problem and the time-dependent navier-stokes equations are presented.
Vector potentials in three-dimensional non-smooth domains
On presente dans cet article un certain nombre de resultats concernant le potentiel vecteur associe a une fonction a divergence nulle dans un ouvert borne de dimension trois. En particulier,…
A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
- B. Rivière, M. Wheeler, V. Girault
- Mathematics, Computer ScienceSIAM Journal on Numerical Analysis
- 1 March 2001
This work analyzes three discontinuous Galerkin approximations for solving elliptic problems in two or three dimensions and proves hp error estimates in the H1 norm, optimal with respect to h, the mesh size, and nearly optimal withrespect to p, the degree of polynomial approximation.
Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
Error analysis of a fictitious domain method applied to a Dirichlet problem
In this paper, we analyze the error of a fictitious domain method with a Lagrange multiplier. It is applied to solve a non homogeneous elliptic Dirichlet problem with conforming finite elements of…
DG Approximation of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition
This work couple the incompressible steady Navier-Stokes equations with the Darcy equations, by means of the Beaver-Joseph-Saffman's condition on the interface, to prove existence of a weak solution as well as some a priori estimates.
A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems
A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems and it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.
Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I
Three Galerkin methods using discontinuous approximation spaces are introduced to solve elliptic problems. The underlying bilinear form for all three methods is the same and is nonsymmetric. In one…
A quasi-local interpolation operator¶preserving the discrete divergence
Abstract: We construct an operator that preserves the discrete divergence and has the same quasi-local approximation properties as a regularizing interpolant; this is very useful when discretizing…