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1.
It is well known that convergence of the fictitious domain formulation with boundary Lagrange multipliers is slow due to the lower global regularity of its solution. This article presents a smoothed variant of this approach which is based on a formulation in the form of a state constraint optimal control problem. The convergence rate is increased as seen from a model example. 相似文献
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对流扩散方程的有限体积-有限元方法的误差估计 总被引:4,自引:1,他引:4
本文结合有限体积方法和有限元方法处理非线性对流扩散问题,非线性对流项利用有限体积方法处理,扩散项利用有限元方法离散,并给近似解的误差估计。 相似文献
3.
The purpose of this paper is to study the convergence of finite element approximation to the exact solution of general self-adjoint elliptic equations with discontinuous coefficients. Due to low global regularity of the solution, it is difficult to achieve optimal order of convergence with classical finite element methods [Numer. Math. 1998; 79:175–202]. In this paper, an isoparametric type of discretization is used to prove optimal order error estimates in L 2 and H 1 norms when the global regularity of the solution is low. The interface is assumed to be of arbitrary shape and is smooth for our purpose. Further, for the purpose of numerical computations, we discuss the effect of numerical quadrature on finite element solution, and the related optimal order estimates are also established. 相似文献
4.
Wolfgang Dahmen Torben Klint Karsten Urban 《Foundations of Computational Mathematics》2008,3(2):135-143
We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl:
Ω{\bf)} derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange
multipliers. Both the time dependent and time harmonic formulations of the Maxwell's equations are considered, and we derive
well-posed formulations for both cases. The variational problem that arises can be discretized by functions that do not satisfy
an a-priori divergence constraint. 相似文献
5.
Hong-xing Rui 《应用数学学报(英文版)》2005,21(3):359-372
Finite volume element method for the Stokes problem is considered. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H^1 norm error estimate. For two widely used dual meshes we give the L^2 norm error estimates, which is optimal in one case and quasi-optimal in another ease. Finally we give a numerical example. 相似文献
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In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method (FVE) based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems. 相似文献
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In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption. 相似文献
9.
本文主要讨论了Stokes问题的非重迭型两仓区域性情形的区域分解算法,首先讨论了连续情形,然后将区域分解算法应用到Stokes问题的非协调离散情形。 相似文献
10.
J. T. Haslinger K. Kunisch G. Peichl 《Computational Optimization and Applications》2003,26(3):231-251
This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers. 相似文献
11.
In this paper,using Lin's integral identity technique,we prove the optimal uniform convergence θ(N_x~(-2)In~2N_x N_y~(-2)In~2N_y) in the L~2-norm for singularly per- turbed problems with parabolic layers.The error estimate is achieved by bilinear fi- nite elements on a Shishkin type mesh.Here N_x and N_y are the number of elements in the x- and y-directions,respectively.Numerical results are provided supporting our theoretical analysis. 相似文献
12.
正交各向异性弹性力学平面问题的样条虚边界元法 总被引:6,自引:0,他引:6
采用域外奇点技术并根据问题的边界条件,建立了正交各向异性弹性力学平面问题的非奇异虚边界积分方程,然后采用性态优越的B样条函数去逼近未知虚荷载函数,并采用性能稳定的最小二乘边界子段法去消除边界余量,据此获得积分方程的数值解.数值算例表明:该方法具有相当高的精度和良好的数值稳定性,且计算工作量少.文中引言部分还对域外奇点法的发展作了系统的评述. 相似文献
13.
本文研究无穷凹角区域上一类各向异性问题的自然边界元法.利用自然边界归化原理,获得该问题的Poisson积分公式和自然积分方程,给出了自然积分方程的数值方法,以及逼近解的收敛性和误差估计,最后给出了数值例子,以示方法的可行性和有效性. 相似文献
14.
We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth
domains in ℝ2. A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated
on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used
to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in
the case where the principal part of the differential operator is the Laplacian.
Online publication 23 January 2004. 相似文献
15.
H. X. Rui 《计算数学(英文版)》1996,14(4):291-300
1.IntroductionDomaindecompositionasanewmethodofcomputationalmathematics,waJsdevel-opedsincethedevelopmentofparallelcomputersandmultiprocessorsupercomputers-Usingdomaindecompositionwecandecreasethescaleoftheproblemandimplementthesub-problemsonparallelcomputer.Fromatechnicalpointofviewmostofdo-maindecompositionmethodsconsideredsofarhavebeendealingwithfiniteelementmethods.In[1,2]ZhangandHuanghavegivenakindofnonoverlappingdomaindecompositionprocedurewithpiecewiselinearfiniteelementapproximation.… 相似文献
16.
Zhong-ciShi Xue-junXu Hong-yingMan 《计算数学(英文版)》2004,22(6):905-920
In this paper, some effective cascadic multigrid methods are proposed for solving the large scale symmetric or nonsymmetric algebraic systems arising from the finite volume methods for second order elliptic problems. It is shown that these algorithms are optimal in both accuracy and computational complexity. Numerical experiments are reported to support our theory. 相似文献
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Fictitious domain method shows great advantages when handling problems with complex and constantly varying domains. In this article, we propose an algorithm which extends the fictitious domain method by introducing penalties. Test results with the numerical examples of backward facing step problem and the flow around steady and dynamic cylinder problem show that the algorithm we propose is highly efficient for solving incompressible fluid problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
20.
文中叙述了具变系数抛物型方程在变动区域中的有限元半离散格式和全离散θ格式,给出了误差界和稳定性结果,并应用于求解Stefan问题。 相似文献