高次Galerkin有限元法的超收敛性

通过局部误差估计,对具有光滑边界的二阶常系数椭圆型方程,给出了高次Ｇａｌｅｒｋｉｎ 有限元法的超收敛性． 运用对称技巧和积分恒等式技巧,在局部对称矩形网格或三角形网格上,我们得到了改进的超收敛性（提高１－ ３ 阶）．     

HIGH ACCURACY ANALYSIS FORINTEGRODIFFERENTIAL EQUATIONS

1.IntroductionLetfibearectangulardomain.WeconsidertheRichardsonextrapolationanddefectcorrectionofthefiniteelementapproximationstothesolutionsofthefollowingsimpleparabolicintegrodifferentialequationsItiswellknownthattheextrapolationmethodsareveryeffectivenumericalmethodsinproducinghigheraccuracyapproximations.Thistechniqueusedforthefiniteelemelltapproximationstothesolutionsofellipticdifferentialequationshasbeenwelldemonstratedin[l--3,5--7,14--18,22and24].Andthistechniquehasalsobeenconsideredfo…     

EXTRAPOLATION AND DEFECT CORRECTION FOR DIFFUSION EQUATIONS WITH BOUNDARY INTEGRAL CONDITIONS

1IntroductionIn[8],we11avestudiedparabolicintegrodifferentialequationswithhomogeneousboundaryconditionsbyextrapolatiollandcorrectionmethods,andderivedGalerkinapproximationsofthirdorder.Nowweturntodiffusionequationswithboundaryintegralconditions.Letfibearectangulardomain.Weareconcernedwitlltheapproximationtothesolutionofthemodelproblemwheren(x,y)=(m(x,y),"Z(x,y))istheouter--normaldirectiononoff.2GlobalExtrapolationFirstofall,wediscussextrpolationfortheproblem(1.l).Throughouttilepaper,weassum…     

Stokes方程最优控制问题超收敛与后验估计

1 引言 Stokes方程最优控制问题在工程应用中有重要的意义,其数值方法的研究受到人们的广泛关注．本文应用重构型超收敛技术得到了超收敛结果和渐进准确的后验误差估计．应用后验误差估计我们还能进行自适应计算．     

Numerical Simulation for Convection-Diffusion Problem with Periodic Micro-Structure

In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution, of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient 5, and it may be convergent independent of δ under some conditions. The numerical results demonstrating the theoretical results are presented in this article.     

基于特征相关网格的不连续Galerkin法

不连续Galerkin法是求解一阶双曲方程的有效方法,然而其解的逼近能否达到丰满阶,(特别是在解不连续的情况下),逼近解的收敛性能否得到保证是理论上尚未解决的问题。针对上述问题,本文提出了特征相关网格,并将其用于不连续的Galerkin法。理论分析和计算结果表明,上述方法可将已有的解的L_2误差估计提高半阶,达