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1.
P. LeTallec 《Numerische Mathematik》1980,35(4):381-404
Summary We study in this paper the convergence of a new mixed finite element approximation of the Navier-Stokes equations. This approximation uses low order Lagrange elements, leads to optimal order of convergence for the velocity and the pressure, and induces an efficient numerical algorithm for the solution of this problem. 相似文献
2.
Nonlinear Galerkin methods and mixed finite elements:
two-grid algorithms for the Navier-Stokes equations 总被引:14,自引:0,他引:14
Summary.
A nonlinear Galerkin method using mixed finite
elements is presented for the two-dimensional
incompressible Navier-Stokes equations. The
scheme is based on two finite element spaces
and for the approximation of the velocity,
defined respectively on one coarse grid with grid
size and one fine grid with grid size and
one finite element space for the approximation
of the pressure. Nonlinearity and time
dependence are both treated on the coarse space.
We prove that the difference between the new
nonlinear Galerkin method and the standard
Galerkin solution is of the order of $H^2$, both in
velocity ( and pressure norm).
We also discuss a penalized version of our algorithm
which enjoys similar properties.
Received October 5, 1993 / Revised version received November
29, 1993 相似文献
3.
Summary In this paper we derive error estimates for a class of finite element approximation of the Stokes equation. These elements, popular among engineers, are conforming lagrangian both in velocity and pressure and therefore based on a mixed variational principle. The error estimates are established from a new Brezzi-type inequality for this kind of mixed formulation. The results are true in 2 or 3 dimensions. 相似文献
4.
《数学季刊》2017,(1)
In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H~1-norm and L~2-norm for velocity as well as the L~2-norm for the pressure are derived. 相似文献
5.
In this paper,a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure.The convergence analysis is presented and optimal error estimates of both broken H1-norm and L2-norm for velocity as well as the L2-norm for the pressure are derived. 相似文献
6.
In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis. 相似文献
7.
Stokes方程的压力梯度局部投影间断有限元法 总被引:2,自引:1,他引:1
本文对定常的Stokes方程提出了一种新的间断有限元法,通过将通常的间断Galerkin有限元法与压力梯度局部投影相结合,建立了一个稳定的间断有限元格式,对速度和压力的任意分片多项式空间P_l(K),P_m(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L~2范数的最优误差估计. 相似文献
8.
Hou-De Han 《计算数学(英文版)》1987,5(2):135-143
In this paper, a new finite element scheme for Navier-Stokes equations is proposed, in which three different partitions (in the two dimensional case) are used to construct finite element subspaces of the velocity field and the pressure. The error estimate of the finite element than approximation is given. The precision of this new scheme has the same order as the scheme $Q_2/P_0$, but it is more economical that the scheme $Q_2/P_0$. 相似文献
9.
A new finite element formulation for two-dimensional viscous flow and convection heat transfer is presented. The current method was designed in particular to be competitive with finite difference methods in terms of storage requirements, solution times, and range of applicability. Novel features of the formulation include the use of a streamline upwind approximation for the advection terms and an equal order velocity and pressure approximation.The current paper focuses on the features of the method which allow the formulation to be competitive with available finite difference methods. The method is illustrated by application to two examples including a natural convection example and a forced convection example. 相似文献
10.
Stokes型积分——微分方程的Galerkin近似 总被引:2,自引:0,他引:2
张铁 《高等学校计算数学学报》1997,19(3):280-285
本文讨论一类具有Stokes方程结构的积分一微分方程的Galerkin近似,论证了近似解的存在唯一性,并分别导出速度和压力近似解的最优阶L_2模误差估计。 相似文献
11.
Summary.
The aim of this work is to study a decoupled algorithm of
a fixed point for solving a
finite element (FE) problem for the approximation of viscoelastic
fluid flow obeying an Oldroyd B differential model. The interest for
this algorithm lies in its applications to numerical simulation and
in the cost of computing. Furthermore it is easy to bring this
algorithm into play.
The unknowns
are
the viscoelastic part of the extra stress tensor,
the velocity and
the pressure.
We suppose that the solution
is sufficiently
smooth and small. The approximation
of stress, velocity and pressure are resp.
discontinuous,
continuous,
continuous FE. Upwinding needed for convection of
, is made
by discontinuous FE. The method consists to
solve alternatively a transport equation for the stress,
and a Stokes like problem for velocity and pressure. Previously,
results of existence of the solution for the approximate problem and
error bounds have been obtained using fixed point
techniques with coupled algorithm.
In this paper we show that the mapping of the decoupled
fixed point algorithm is locally (in a neighbourhood of
)
contracting and we obtain existence, unicity (locally) of the solution
of the approximate problem and error bounds.
Received
July 29, 1994 / Revised version received March 13, 1995 相似文献
12.
Summary We propose a multidomain spectral collocation scheme for the approximation of the two-dimensional Stokes problem. We show that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.Deceased 相似文献
13.
Discontinuous Stable Elements for the Incompressible Flow 总被引:4,自引:0,他引:4
Xiu Ye 《Advances in Computational Mathematics》2004,20(4):333-345
In this paper, we derive a discontinuous Galerkin finite element formulation for the Stokes equations and a group of stable elements associated with the formulation. We prove that these elements satisfy the new inf–sup condition and can be used to solve incompressible flow problems. Associated with these stable elements, optimal error estimates for the approximation of both velocity and pressure in L
2 norm are obtained for the Stokes problems, as well as an optimal error estimate for the approximation of velocity in a mesh dependent norm. 相似文献
14.
The aim of the present paper is to study the propagation of a variable energy blast wave (cylindrical) through a gas having solid-body rotation. The modified similarity method has been used to obtain the first, second and third approximation solutions. The analysis shows that the effects of solid-body rotation on the flow are of third order. Variation of pressure, density and radial velocity distributions with initial angular velocity has been discussed. 相似文献
15.
Endre Süli 《Numerische Mathematik》1988,53(4):459-483
Summary The Lagrange-Galerkin method is a numerical technique for solving convection — dominated diffusion problems, based on combining a special discretisation of the Lagrangian material derivative along particle trajectories with a Galerkin finite element method. We present optimal error estimates for the Lagrange-Galerkin mixed finite element approximation of the Navier-Stokes equations in a velocity/pressure formulation. The method is shown to be nonlinearly stable. 相似文献
16.
Joe Koebbe 《Numerical Methods for Partial Differential Equations》1993,9(4):339-355
The mixed finite element method for approximately solving flow equations in porous media has received a good deal of attention in the literature. The main idea is to solve for the head/pressure and fluid velocity (Darcy velocity) simultaneously to obtain a higher order approximation of the fluid velocity. In the case of a diagonal transmissivity tensor the algebraic equations resulting from the discretization can be reduced to a system of algebraic equations for the head/pressure variable alone. This reduction results in a smaller number of unknows to be solved for in an iterative method such as preconditioned conjugate gradient method. The fluid velocity is then obtained from an algebraic relationship. In the case of full transmissivity tensor, the algebraic reduction is more difficult. This paper investigates some algorithms resulting from the modification of the mixed finite element that take advantage of the mixed finite element method for the diagonal tensor case. The resulting schemes are more efficient implementations that maintain the same order of accuracy as the original schemes. © 1993 John Wiley & Sons, Inc. 相似文献
17.
Summary. This is the third paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate
elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous
media. In this paper we consider a finite element approximation for this system. The elliptic equation for the pressure and
velocity is approximated by a mixed finite element method, while the degenerate parabolic equation for the saturation is approximated
by a Galerkin finite element method. A fully discrete approximation is analyzed. Sharp error estimates in energy norms are
obtained for this approximation. The error analysis does not use any regularization of the saturation equation; the error
estimates are derived directly from the degenerate equation. Also, the analysis does not impose any restriction on the nature
of degeneracy. Finally, it respects the minimal regularity on the solution of the differential system.
Received March 9, 1998 / Revised version received July 17, 2000 / Published online May 30, 2001 相似文献
18.
1. IntroductionIn the numerical approximation of PDE, it is often very importals to detect regionswhere the accuracy of the numerical solution is degraded by local singularities of the solutionof the continuous problem such as the singularity near the re-entrant corller. An obviousremedy is to refine the discretization in the critical regions, i.e., to place more gridpointswhere the solution is less regular. The question is how to identify these regions automdticallyand how to determine a goo… 相似文献
19.
A simple nonconforming brick element is proposed for 3D Stokes equations. This element has 15 degrees of freedom and reaches the lowest approximation order. In the mixed scheme for Stokes equations, we adopt our new element to approximate the velocity, along with the discontinuous piecewise constant element for the pressure. The stability of this scheme is proved and thus the optimal convergence rate is achieved. A numerical example verifies our theoretical analysis. 相似文献
20.
《中国科学 数学(英文版)》2017,(8)
This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1(k 0) and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k + 1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results. 相似文献