依赖时间的发展方程半离散Galerkin解法的误差估计

其中A(t)=L_1(t)+L_2(t)依赖于时间t。当L_1(t)正定,L_1~(-1)(t)L_2(t)全连续时,我们就一种修正的Galerkin方法,给出了它的解及其关于时间t的各阶导数的误差的H-模估计。     

非线性抛物方程广义差分法的误差估计

设Ω是平面上的有界区域,具有光滑边界?Ω;t~*>0为一常数,T=[0,t~＊].考虑如下的非线性抛物方程:     

非定常 N-S 方程的非线性 Galerkin 算法及其误差估计

本文给出了二维非定常N-S方程的三种数值格式,其中空间变量用谱非线性Galerkin算法进行离散,时间变量用有限差分离散,并研究了这些格式数值解的逼近精度．最后,给出了部分数值计算结果．     

抛物型问题半离散Galerkin近似解的L_∞估计

考察典型的抛物型问题:其中Ω为平面有界区域.设S_h?H_1~0(Ω)是在正规剖分上由分片m-1次多项式构成的有限元空间,其半离散Galerkin逼近可由下式确定:     

非线性抛物方程耦合的离散化及其误差分析

0　引　　言对于线性抛物型初边值问题的有限元与边界元耦合法,我们已作过研究(可参见[2],[3]).然而,许多实际问题,如流体、对流扩散、热辐射及热传输等涉及到非线性问题,因此研究非线性问题的数值方法显得尤为重要.近年来,G.N.Gatica与G.C.Hsiao已将有限元(FEM)与边界元(BEM)耦合法拓广到非线性椭圆问题(如[5],[6]),但如何应用FEM与BEM耦合法来处理非线性抛物型初边值问题,就作者所知迄今为止尚属空白.这里我们试图对此进行研究.设Ω为R2中一有界单连通区域,其边界为Γ:=Ω.Ωc:=R2\Ω为闭区域Ω的补区域,I:=(0,T].我们考虑如…     

非线性抛物方程的时空有限元方法的误差估计

1 引言 本文考虑如下形式的方程 其中,Ω∈R2,0<α≤a(u)≤β,|▽a(u)|≤M,α,βM为正常数.函数f(u)满足:|f(u)|≤ c|u|, (?)∈C(Ω),c为正常数.而且,f(u)是Lipschitz连续函数,即满足|f(u)-|f(v)|≤ L|u-v|,(?)u,v∈C(Ω),L为Lipschitz常数. 利用自适应时空有限元方法求解上述类型的抛物方程,文[1]中对线性模型进行了讨 论,并给出空间L2模误差估计.在[2]中,首次给出了抛物型问题自适应方法的有效性和 可靠性分析,并给出最优L∞(L2)和L∞(L∞o)模误差估计.进一步,[3]3中推广到一般非线     

半线性抛物方程的时空有限元方法的误差估计

<正>1引言本文考虑如下半线性抛物方程(?)其中Ω∈R~2.函数f(u):C→C满足:(1)|f(u)|≤c|u|(?)u∈C(Ω)(2)Lipschitz条件,即     

一类非线性抛物型方程的广义Galerkin方法

本文研究一类非线性二维二阶抛物型方程混合问题的广义Galerkin方法(即广义差分法)讨论了半离散化和全离散化方程的收敛性和稳定性,并得到与有限元方法相同的最佳收敛阶。     

解抛物型方程的半离散精细积分法

本讨论抛物型方程混合问题的解法．提出在有限元半离散过程后，用精细积分法获得一个较好的解，并且分析了这种方法的误差，证明了用这种方法和二次插值，在节点上有O(h^4)的超收敛性．     

Non-Classical Elliptic Projections and $L^2$-Error Estimates for Galerkin Methods for Parabolic Integro-Differential Equations

In this paper we shall define a so-called "non-classical" elliptic projection associated with an integro-differential operator. The properties of this projection will be analyzed and used to obtain the optimal $L^2$ error estimates for the continuous and discrete time Galerkin procedures when applied to linear integro-differential equations of parabolic type.     

A Posteriori Error Estimates of Mixed Methods for Parabolic Optimal Control Problems

In this article, we shall give a brief review on the fully discrete mixed finite element method for general optimal control problems governed by parabolic equations. The state and the co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control is approximated by piecewise constant elements. Furthermore, we derive a posteriori error estimates for the finite element approximation solutions of optimal control problems. Some numerical examples are given to demonstrate our theoretical results.     

非线性抛物型方程组的二次有限体积元方法及其误差估计

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。     

Strong-Norm Error Estimates for the Projective-Difference Method for Parabolic Equations with Modified Crank--Nicolson Scheme

A parabolic problem in a separable Hilbert space is solved approximately by the projective-difference method. The problem is discretized with respect to space by the Galerkin method and with respect to time by the modified Cranck--Nicolson scheme. In this paper, we establish efficient (in time and space) strong-norm error estimates for approximate solutions. These estimates allow us to obtain the rate of convergence with respect to time of the error to zero up to the second order. In addition, the error estimates take into account the approximation properties of projective subspaces, which is illustrated for subspaces of finite element type.     

Schauder Estimates for Elliptic and Parabolic Equations

In this note the author gives an elementary and simple proof for the Schauder estimates for elliptic and parabolic equations. The proof also applies to nonlinear equations.