共查询到20条相似文献,搜索用时 15 毫秒
1.
Jianhong Yang Lei Gang & Jianwei Yang 《advances in applied mathematics and mechanics.》2014,6(5):663-679
In this paper, we consider a two-scale stabilized finite volume method for the two-dimensional
stationary incompressible flow approximated by the lowest equal-order element pair $P_1-P_1$
which does not satisfy the inf-sup condition. The two-scale method consists of solving a small non-linear system
on the coarse mesh and then solving a linear Stokes equations on the fine mesh. Convergence of the optimal
order in the $H^1$-norm for velocity and the $L^2$-norm for pressure is obtained. The error analysis shows
there is the same convergence rate between the two-scale stabilized finite volume solution and the usual
stabilized finite volume solution on a fine mesh with relation $h =\mathcal{O}(H^2)$. Numerical experiments completely
confirm theoretic results. Therefore, this method presented in this paper is of practical importance in
scientific computation. 相似文献
2.
This paper is concerned with a stabilized finite element method
based on two local Gauss integrations for the two-dimensional
non-stationary conduction-convection equations by using the lowest
equal-order pairs of finite elements. This method only offsets the
discrete pressure space by the residual of the simple and symmetry
term at element level in order to circumvent the inf-sup condition.
The stability of the discrete scheme is derived under some
regularity assumptions. Optimal error estimates are obtained by
applying the standard Galerkin techniques. Finally, the numerical
illustrations agree completely with the theoretical expectations. 相似文献
3.
离散元与有限元结合的多尺度方法及其应用 总被引:11,自引:0,他引:11
在深入研究复杂结构和非均质材料冲击响应和破坏机理的过程中,往往遇到多尺度计算问题.提出并建立起离散元与有限元结合的多尺度方法,该方法采用离散元对感兴趣的局部进行细观尺度的模拟,利用有限元进行宏观的模拟,从而节约了计算时间.采用一种特殊的过渡层衔接离散元区和有限元区.将这一方法应用于激光辐照下预应力铝板的破坏响应,并将得到的模拟结果与实验进行了比较. 相似文献
4.
In this paper, based on the stabilization technique, the Oseen iterative method and the two-level finite element algorithm are combined to numerically solve the stationary incompressible magnetohydrodynamic (MHD) equations. For the low regularity of the magnetic field, when dealing with the magnetic field sub-problem, the Lagrange multiplier technique is used. The stabilized method is applied to approximate the flow field sub-problem to circumvent the inf-sup condition restrictions. One- and two-level stabilized finite element algorithms are presented, and their stability and convergence analysis is given. The two-level method uses the Oseen iteration to solve the nonlinear MHD equations on a coarse grid of size H, and then employs the linearized correction on a fine grid with grid size h. The error analysis shows that when the grid sizes satisfy , the two-level stabilization method has the same convergence order as the one-level one. However, the former saves more computational cost than the latter one. Finally, through some numerical experiments, it has been verified that our proposed method is effective. The two-level stabilized method takes less than half the time of the one-level one when using the second class Nédélec element to approximate magnetic field, and even takes almost a third of the computing time of the one-level one when adopting the first class Nédélec element. 相似文献
5.
Yinnian He 《Entropy (Basel, Switzerland)》2021,23(12)
In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair . The method consists of transmitting the finite element solution of the 3D steady Navier–Stokes equations into the finite element solution pairs based on the finite element space pair of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair satisfies the discrete inf-sup condition in a 3D domain . Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to of the FE solution to the exact solution of the 3D steady Navier–Stokes equations in the norm. Finally, we also give the convergence order with respect to of the FE velocity to the exact velocity u of the 3D steady Navier–Stokes equations in the norm. 相似文献
6.
An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations 下载免费PDF全文
Ying Yang & Benzhuo Lu 《advances in applied mathematics and mechanics.》2013,5(1):113-130
Poisson-Nernst-Planck
equations are a coupled system of nonlinear partial differential
equations consisting of the Nernst-Planck equation and
the electrostatic Poisson equation with delta distribution sources,
which describe the electrodiffusion of ions in a solvated
biomolecular system. In this paper, some error bounds for a piecewise
finite element approximation to this problem are derived. Several numerical
examples including biomolecular problems are shown to support our analysis. 相似文献
7.
A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations 下载免费PDF全文
Sufang Zhang Hongxia Yan & Hongen Jia 《advances in applied mathematics and mechanics.》2016,8(3):386-398
In this paper, we study a new stabilized method based on the local pressure
projection to solve the semi-linear elliptic equation. The proposed scheme combines
nonconforming finite element pairs NCP1−P1triangle element and two-level method,
which has a number of attractive computational properties: parameter-free, avoiding
higher-order derivatives or edge-based data structures, but have more favorable stability
and less support sets. Stability analysis and error estimates have been done. Finally,
numerical experiments to check estimates are presented. 相似文献
8.
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10.
11.
In this work, two-level stabilized finite volume formulations for the
2D steady Navier-Stokes equations are considered.
These methods are based
on the local Gauss integration technique and the lowest equal-order
finite element pair. Moreover, the two-level
stabilized finite volume methods involve solving one small Navier-Stokes
problem on a coarse mesh with mesh size $H$, a large general Stokes problem for the Simple and
Oseen two-level stabilized finite volume methods on the fine mesh with mesh size $h$=$\mathcal{O}(H^2)$ or a large general Stokes equations for the Newton two-level stabilized finite
volume method on a fine mesh with mesh size $h$=$\mathcal{O}(|\log h|^{1/2}H^3)$.
These methods we studied provide an
approximate solution $(\widetilde{u}_h^v,\widetilde{p}_h^v)$ with the convergence rate of same order
as the standard stabilized finite volume method, which involve solving one large
nonlinear problem on a fine mesh with mesh size $h$. Hence, our methods
can save a large amount of computational time. 相似文献
12.
13.
In this paper, four stabilized methods based on the lowest equal-order finite element pair for the steady micropolar Navier–Stokes equations (MNSE) are presented, which are penalty, regular, multiscale enrichment, and local Gauss integration methods. A priori properties, existence, uniqueness, stability, and error estimation based on Fem approximation of all the methods are proven for the physical variables. Finally, some numerical examples are displayed to show the numerical characteristics of these methods. 相似文献
14.
15.
Zhendong Luo 《advances in applied mathematics and mechanics.》2014,6(5):615-636
A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme. 相似文献
16.
A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem 下载免费PDF全文
We construct a finite volume element method based on the constrained
nonconforming rotated Q1-constant element (CNRQ1-P0) for the Stokes problem.
Two meshes are needed, which are the primal mesh and the dual mesh. We approximate
the velocity by CNRQ1 elements and the pressure by piecewise constants.
The errors for the velocity in the H1 norm and for the pressure in the L2 norm are
O(h) and the error for the velocity in the L2 norm is O(h2). Numerical experiments
are presented to support our theoretical results. 相似文献
17.
二维多介质可压缩流的RKDG有限元方法 总被引:1,自引:0,他引:1
应用RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法、Level Set方法和Ghost Fluid方法数值模拟二维多介质可压缩流,其中Euler方程组、Level Set方程和重新初始化方程的空间离散采用DG(Discontinuous Galerkin)有限元方法,时间离散采用Runge-Kutta方法.对二维的气-气和气-液两相流进行了数值计算,得到了分辨率较高的计算结果. 相似文献
18.
Yunqing Huang Jichun Li & Yanping Lin 《advances in applied mathematics and mechanics.》2013,5(4):494-509
In this paper, the time-dependent Maxwell's equations used to modeling
wave propagation in dispersive lossy bi-isotropic media are investigated.
Existence and uniqueness of the modeling equations are proved.
Two fully discrete finite element schemes are proposed, and their practical
implementation and stability are discussed. 相似文献
19.
20.
An Iterative Two-Grid Method of a Finite Element PML Approximation for the Two Dimensional Maxwell Problem 下载免费PDF全文
Chunmei Liu Shi Shu Yunqing Huang Liuqiang Zhong & Junxian Wang 《advances in applied mathematics and mechanics.》2012,4(2):175-189
In this paper, we propose an iterative two-grid method for the edge finite
element discretizations (a saddle-point system) of Perfectly Matched Layer (PML)
equations to the Maxwell scattering problem in two dimensions. Firstly, we use
a fine space to solve a discrete saddle-point system of $H(grad)$ variational problems,
denoted by auxiliary system 1. Secondly, we use a coarse space to solve the
original saddle-point system. Then, we use a fine space again to solve a discrete$\boldsymbol{H}(curl)$-elliptic variational problems, denoted by auxiliary system 2. Furthermore,
we develop a regularization diagonal block preconditioner for auxiliary system 1
and use $H$-$X$ preconditioner for auxiliary system 2. Hence we essentially transform
the original problem in a fine space to a corresponding (but much smaller)
problem on a coarse space, due to the fact that the above two preconditioners are
efficient and stable. Compared with some existing iterative methods for solving
saddle-point systems, such as PMinres, numerical experiments show the competitive
performance of our iterative two-grid method. 相似文献