双曲型方程的质量集中有限元法

用有限元法求解波动方程有许多工作,在此不多加阐述,本文针对线性双曲型方程采用质量集中有限元法,该方法产生于用特定的数值积分公式计算普通有限元法中的内积积分,这种方法具有较好的数值稳定性。     

用Tikhonov正则化方法求一阶和两阶的数值微分

Numerical differentiation is an ill-posed problem, which is important in scientific research and practical applications.In this paper, we use the Tikhonov regularization method to discuss the first and secord order derivatives of a smooth function. The error estimate is also given. And the numerical results prove that our method is applicable.     

关于一类二阶非线性双曲型方程全离散有限元方法的稳定性和收敛性估计

1　引　　言考虑如下混合问题 :φ( x,u) utt- di,j=1 xi( aij( x,u) u xj) - di=1bi( x,u) uxi =f( x,u)　　　　　　　　　　　　　　　 ( x,t)∈Ω× [0 ,T]u( x,0 ) =0 ,　 ut( x,0 ) =0　　 x∈Ωu( x,t) =0　 ( x,t)∈ Ω× [0 ,T]( 1 .1 )这里 utt= 2 u t2 ,uxi= u xi;Ω是 Rd 中充分光滑的有界开域 ,边界 Ω光滑 .对于 φ( x,u)中仅含有 x,或 φ( x,u)≡ 1的线性或非线性双曲型方程的半离散或全离散有限元方法的研究已有 [1 ] -[4 ] .这些文献定义了线性[1 ] [4] 或非线性[2 ] 或预测—校正[4] 全离散有限元格式 ,然后将原方…     

水污染问题特征有限元方法的数值计算及理论分析

本文研究了水污染二维对流占优数学模型特征有限元方法的计算问题，导出的计算格式对时间变量用特征线方法离散，对空间变量用Galerkin有限元方法离散，得到的H^1－模和L^2－模误差估计是最优阶的。     

THE L~2-NORM ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT METHOD FOR THE 2ND ORDER ELLIPTIC PROBLEM WITH THE LOWEST REGULARITY

1. IntroductionThis paper is concerned with the uniformly LZ-- norm error estimate of the nonconforming finite method for the second order elliptic problem with the lowest regularity3i.e., in the case that the solution u E H'(fl) only, but not in H'(fl).For the conforming finite element method of the second order elliptic problem, it iswell known that using the Aubin-Nitsche lemma obtained the LZ-- norm error bound,which is one order of h, the parameter of triangulation, higher than the HI…     

THE OPTIMAL CONVERGENCE ORDER OF THE DISCONTINUOUS FINITE ELEMENT METHODS FOR FIRST ORDER HYPERBOLIC SYSTEMS

In this paper, a discontinuous finite element method for the positive and symmetric, first-order hyperbolic systems （steady and nonsteady state） is constructed and analyzed by using linear triangle elements, and the O（h^2）-order optimal error estimates are derived under the assumption of strongly regular triangulation and the Ha-regularity for the exact solutions. The convergence analysis is based on some superclose estimates of the interpolation approximation. Finally, we discuss the Maxwell equations in a two-dimensional domain, and numerical experiments are given to validate the theoretical results.     

二阶椭圆问题新的混合元格式

本文基于二阶椭圆问题一种新的混合变分形式,给出同时满足强椭圆性和B-B条件的任意次的求解格式.理论分析表明这些单元论证简单而且用了较少的自由度达到最优误差估计.同时我们还给出了它们在各向异性网格下的误差估计.     

QUASI-CONFORMING FINITE ELEMENT APPROXIMATION FOR A FOURTH ORDER VARIATIONAL INEQUALITY WITH DISPLACEMENT OBSTACLE

In this paper, unconventional quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle is considered, the optimal order of error estimate O(h) is obtained which is as same as that of the conventional finite elements.     

Sine-Gordon方程的一类低阶非协调有限元分析

本文讨论了Sine-Gordon方程的一类低阶非协调有限元一般逼近格式,直接利用插值技巧和单元的特殊性质导出了相应未知量的最优误差估计.     

A POSTERIORI ERROR ESTIMATES FOR A MODIFIED WEAK GALERKIN FINITE ELEMENT APPROXIMATION OF SECOND ORDER ELLIPTIC PROBLEMS WITH DG NORM

In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuous Galerkin methods still gives both upper and lower bounds for the modified weak Galerkin method,though they have essentially different bilinear forms.More precisely,we prove its reliability and efficiency for the actual error measured in the standard DG norm.We further provide an improved a priori error estimate under minimal regularity assumptions on the exact solution.Numerical results are presented to verify the theoretical analysis.     

THE CONVERGENCE ON A FAMILY OF ITERATIONS WITH CUBIC ORDER

1. IntroductionLet E and F be real or complex Banach spaces and f: D G E --+ F be a nonlinar twicediffereotiable operator. FOr solving the eqwtionconsider a one-parametered edly of iterationswhere Hj(x) = f'(x)--'f,,(x)j'(x)--'f(x) and 0 S A 5 1. This hal is cubically convergent(see [3, 7] ) and includes, as particular cases, Chebyshev method (^ = 0, see [5, 9l), Halleymethod (A = l, see [1, 4, 6, 10]) and suPer-Halley method (A = 1, see [7]).In [3], I.K. AIgyros et al analyze the con…     

ORDER RESULTS OF GENERAL LINEAR METHODS FOR MULTIPLY STIFF SINGULAR PERTURBATION PROBLEMS

In this paper we analyze the error behavior of general linear methods applied to some classes of one-parameter multiply stiff singularly perturbed problems. We obtain the global error estimate of algebraically and diagonally stable general linear methods. The main result of this paper can be viewed as an extension of that obtained by Xiao [13] for the case of Runge-Kutta methods.     

一类奇异非线性两点边值问题的 Galerkin 解的误差估计

本文对一类奇异两点边值问题采用了对称的Galerkin方法.通过利用Green函数,对线性问题得到了拟最优的最大范数误差估计并将这一结果推广到了非线性问题.本文最后列举了一些数值试验结果,这些结果很好地验证了理论结果.     

Backus—Gilbert方法对不精确数据解的误差估计

1 引言 1968年地质学家G Backus and F Gilbert给出了求解线性(非线性)矩问题的一种方法,用来求解地球物理反问题。后来称这种方法为B-G方法。过去几年,数学家们从理论和应用方面研究了B-G方法。从理论上分析了其收敛性并给出了误差估计。第一类算子方程在不同函数空间的离散化得到不同形式的矩问题。[4]、[5]研究了再生核空间和小波空间的B-G方法。并用于信号恢复问题。由于矩问题的不适定性,有必要分析B-G方法解的正则性,本文得到了B-G方法对不精确数据的误差估计,从而证明了B-G方法是—种正则化方法。 考虑线性矩问题     

Pointwise error estimates of the local discontinuous Galerkin method for a second order elliptic problem

In this paper we derive some pointwise error estimates for the local discontinuous Galerkin (LDG) method for solving second-order elliptic problems in (). Our results show that the pointwise errors of both the vector and scalar approximations of the LDG method are of the same order as those obtained in the norm except for a logarithmic factor when the piecewise linear functions are used in the finite element spaces. Moreover, due to the weighted norms in the bounds, these pointwise error estimates indicate that when at least piecewise quadratic polynomials are used in the finite element spaces, the errors at any point depend very weakly on the true solution and its derivatives in the regions far away from . These localized error estimates are similar to those obtained for the standard conforming finite element method.

     

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES

In this paper we show that in error estimates, the condition number k(T) of any in-vertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Ba-nach theorem and other related results.     

LOCAL A PRIORI AND A POSTERIORI ERROR ESTIMATE OF TQC9 ELEMENT FOR THE BIHARMONIC EQUATION

In this paper, local a priori, local a posteriori and global a posteriori error estimates are obtained for TQC9 element for the biharmonic equation. An adaptive algorithm is given based on the a posteriori error estimates.     

热传导—对流问题的混合有限元分析注记

本文研究流体力学中的热传导－对流问题,分析其混合有限元解的存在性和误差估计,并给出一些混合有限元格式的例子。     

SCHWARZ-PICK ESTIMATES FOR PARTIAL DERIVATIVES OF ARBITARY ORDER OF BOUNDED HOLOMORPHIC FUNCTIONS IN THE UNIT BALL OF C~n

This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of C n .