共查询到20条相似文献,搜索用时 15 毫秒
1.
芮洪兴 《数学物理学报(B辑英文版)》2004,24(1):129-138
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H^1 norm error estimates are given. 相似文献
2.
《Journal of Computational and Applied Mathematics》2002,146(2):373-386
The finite volume element method is a discretization technique for partial differential equations, but in general case the coefficient matrix of its linear system is not symmetric, even for the self-adjoint continuous problem. In this paper we develop a kind of symmetric modified finite volume element methods both for general self-adjoint elliptic and for parabolic problems on general discretization, their coefficient matrix are symmetric. We give the optimal order energy norm error estimates. We also prove that the difference between the solutions of the finite volume element method and symmetric modified finite volume element method is a high order term. 相似文献
3.
M. Stojanović 《分析论及其应用》1996,12(2):86-98
We perform analysis for a finite elements method applied to the singular self-adjoint problem. This method uses continuous
piecewise polynomial spaces for the trial and the test spaces. We fit the trial polynomial space by piecewise exponentials
and we apply so exponentially fitted Galerkin method to singular self-adjoint problem by approximating driving terms by Lagrange
piecewise polynomials, linear, quadratic and cubic. We measure the erroe in max norm. We show that method is optimal of the
first order in the error estimate. We also give numerical results for the Galerkin approximation. 相似文献
4.
P. Chatzipantelidis R. D. Lazarov V. Thome 《Numerical Methods for Partial Differential Equations》2004,20(5):650-674
We analyze the spatially semidiscrete piecewise linear finite volume element method for parabolic equations in a convex polygonal domain in the plane. Our approach is based on the properties of the standard finite element Ritz projection and also of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite volume element method. Because the domain is polygonal, special attention has to be paid to the limited regularity of the exact solution. We give sufficient conditions in terms of data that yield optimal order error estimates in L2 and H 1 . The convergence rate in the L∞ norm is suboptimal, the same as in the corresponding finite element method, and almost optimal away from the corners. We also briefly consider the lumped mass modification and the backward Euler fully discrete method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 相似文献
5.
In this paper, we study the Crank-Nicolson Galerkin finite element method and construct a two-grid algorithm for the general two-dimensional time-dependent Schrödinger equation. Firstly, we analyze the superconvergence error estimate of the finite element solution in $H^1$ norm by use of the elliptic projection operator. Secondly, we propose a fully discrete two-grid finite element algorithm with Crank-Nicolson scheme in time. With this method, the solution of the Schrödinger equation on a fine grid is reduced to the solution of original problem on a much coarser grid together with the solution of two Poisson equations on the fine grid. Finally, we also derive error estimates of the two-grid finite element solution with the exact solution in $H^1$ norm. It is shown that the solution of two-grid algorithm can achieve asymptotically optimal accuracy as long as mesh sizes satisfy $H = \mathcal{O}(h^{\frac{1}{2}})$. 相似文献
6.
Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations 总被引:1,自引:0,他引:1
In this paper, a cubic superconvergent finite volume element method based on optimal stress points is presented for one-dimensional elliptic and parabolic equations. For elliptic problem, it is proved that the method has optimal third order accuracy with respect to H1 norm and fourth order accuracy with respect to L2 norm. We also obtain that the scheme has fourth order superconvergence for derivatives at optimal stress points. For parabolic problem, the scheme is given and error estimate is obtained with respect to L2 norm. Finally, numerical examples are provided to show the effectiveness of the method. 相似文献
7.
The finite element method is applied through the use of a variational inequality to an obstacle problem involving nonhomogeneous boundary data. For piecewise linear conforming trial functions energy norm error bounds are derived. 相似文献
8.
Panagiotis Chatzipantelidis 《Numerische Mathematik》1999,82(3):409-432
We introduce and analyse a finite volume method for the discretization of elliptic boundary value problems in . The method is based on nonuniform triangulations with piecewise linear nonconforming spaces. We prove optimal order error
estimates in the –norm and a mesh dependent –norm.
Received September 10, 1997 / Revised version received March 18, 1998 相似文献
9.
We consider an interior point method in function space for PDE constrained optimal control problems with state constraints.
Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive
grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error
of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required
Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose
we propose an a-posteriori error estimator for a problem suited norm. 相似文献
10.
In this article, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints. A priori error estimates of optimal order are derived for velocity and pressure in the energy norm and the L2-norm, respectively. Moreover, a reliable and efficient a posteriori error estimator is derived. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. In particular, we consider the abstract results with suitable stable pairs of velocity and pressure spaces like as the lowest-order Crouzeix–Raviart finite element and piecewise constant spaces, piecewise linear and constant finite element spaces. The theoretical results are illustrated by the numerical experiments. 相似文献
11.
Ruo Li & Fanyi Yang 《计算数学(英文版)》2023,41(1):39-71
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by the patch reconstruction with one unknown per element. For the first step, we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero trace. By this space, we minimize a least squares functional to obtain the numerical approximations to the gradient of the velocity and the pressure. In the second step, we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free space. We derive error estimates for all unknowns under both $L^2$ norms and energy norms. Numerical results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method. 相似文献
12.
Cascadic multigrid technique for mortar Wilson finite element method of homogeneous boundary value planar linear elasticity is described and analyzed. First the mortar Wilson finite element method for planar linear elasticity will be analyzed, and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigrid method for the mortar finite element discrete problem is described. Suitable grid transfer operator and smoother are developed which lead to an optimal cascadic multigrid method. Finally, the computational results are presented. 相似文献
13.
Error analysis of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation 下载免费PDF全文
Huipo Liu Shuanghu Wang Hongbin Han Lan Yuan 《Numerical Methods for Partial Differential Equations》2017,33(5):1493-1512
This article discusses a priori and a posteriori error estimates of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation. We use variational discretization concept to discretize the control variable and discontinuous piecewise linear finite elements to approximate the state and costate variable. Based on the error estimates of discontinuous Galerkin finite element method for the transport equation, we get a priori and a posteriori error estimates for the transport equation optimal control problem. Finally, two numerical experiments are carried out to confirm the theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1493–1512, 2017 相似文献
14.
讨论基于三角形网格的二维非线性抛物型方程组的有限体积元方法,其中试探函数空间为二次Lagrange元,检验函数空间为分片常数函数空间,对问题的全离散格式证明了最优的能量模误差估计。最后给出一个相关数值算例以验证格式的有效性。 相似文献
15.
N. Yu. Bakaev 《BIT Numerical Mathematics》1997,37(2):237-255
The maximum norm error estimates of the Galerkin finite element approximations to the solutions of differential and integro-differential
multi-dimensional parabolic problems are considered. Our method is based on the use of the discrete version of the elliptic-Sobolev
inequality and some operator representations of the finite element solutions. The results of the present paper lead to the
error estimates of optimal or almost optimal order for the case of simplicial Lagrangian piecewise polynomial elements. 相似文献
16.
非定常Navier-Stokes方程的稳定化特征有限元法 总被引:1,自引:0,他引:1
1引言特征线有限元法是求解对流扩散问题的有效方法。在处理对流占优问题时,表现出了很好的稳定性[8]。对于求解Navier-Stokes方程,文[9]建立了特征有限元格式,并进行了详细分析,但得到的收敛阶O(h~m △t (h~(m 1)/△t))只是拟丰满的。文[10]对此作了非线性稳定性的进一步分析,给出了关于速度和压力的最优误差估计。但目前所有的特征有限元法都要求有限元空间满足inf-sup条件,这就排除了工程实际应用计算方便的低阶有 相似文献
17.
In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H^1 norm error estimates. A numerical example is given at the end to show the feasibility of the method. 相似文献
18.
In this paper, we present a finite volume framework for second order elliptic equations with variable coefficients based on cubic Hermite element. We prove the optimal H1 norm error estimates. A numerical example is given at the end to show the feasibility of the method. 相似文献
19.
In this paper we prove the possibility of the use of the penalty method for grid matching in mixed finite element methods. We consider the Hermann-Johnson scheme for biharmonic equation. The main idea is to construct a perturbed problem with two parameters which play roles of penalties. The perturbed problem is built by the replacement of essential conditions on the interface in the mixed variational statement with natural conditions that contain parameters. The perturbed problem is discretized by the finite element method. We estimate the norm of the difference between a solution of the discrete perturbed problem and a solution of the initial problem; the obtained estimates depend on the step and the penalties. We give recommendations for the choice of penalties depending on the step. 相似文献
20.
In this paper we study the convergence of an adaptive finite element method for optimal control problems with integral control constraint. For discretization, we use piecewise constant discretization for the control and continuous piecewise linear discretization for the state and the co-state. The contraction, between two consecutive loops, is proved. Additionally, we find the adaptive finite element method has the optimal convergence rate. In the end, we give some examples to support our theoretical analysis. 相似文献