L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID （EXCMG）

Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.     

SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the underlying problem. Unconditional L2-stability and error estimate of order O τr+1+ hk+1/2 are obtained when polynomials of degree at most r and k are used for the temporal discretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r + 1 in temporal variable t.     

AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES

This article will combine the finite element method, the interpolated coefftcient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.     

EXISTENCE OF MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

1 IntroductionWe deal with the problem{ it:;,."--'"'::3of (11)where 9 C RN, N 2 3 is a bounded domain with smooth boundary 0fl, 0n = ro U r1, ro andYl have (N -- 1)-dinlensiollal Hausdorff nleasuret r E L'(r1), yt 2 0, V * 0 on r1, 7 denotesthe u11it outward normal and p = 2* = ee is the critical SoboleY exponent fOr the Sobolevembedding V(O) - H(O), V(fl) = {u E H'(fl) l u = 0 on ro}'The case ro and r1 have positive (N -- 1)-dimellsional Hausdoor measure aud p = 0on r1 in (1.1), has…     

求非线性问题多解的搜索延拓法

基于-Δ的特征系λ_j,φ_j,逼近非线性问题 Δu+f(u)=0(在Ω中), u=0(在¶Ω上)的多重解. 提出了一种新的搜索延拓法(SEM),它由三层子空间上的三种算法组成. 对f(u)=u³,在正方形和L形区域上完成了数值实验.这些结果表明,对应于-Δ的每个k重特征值, 至少存在3^k-1个不同的非零解(猜想1).     

ON NEUMANN PROBLEM FOR SOMESEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

1IntroductionLetnbeaboundeddomaininRewithCIboundarytn23.Weconsidertheprobleminwhichp=ac,q=M,7denotestheunitoutwardnormaltoon,A>0,p20.Inthisp8Per,wesuppose(Al)a(z)eL"(n),a(z)50.(afl)op(2)EC(on),op(x)20,M==op(:).(op2)op(zo)=M,icEOf.InasmallneighborhoodUofic,thedoesnQliesononesideOfthetangentplaneOfonatic,andthe(n--l)principlecurvaturesofxo(withrespecttotheinnernormalOfon)arepositive.(gi)g(z,u)ismeasurablein2,continuousinu,sup{g(2,u)::En,0Su5an}< coforeveryfixedan>0andg(x,0)=0.(g2)!5op=0…     

外推瀑布多网格法(EXCMG)——-大规模求解椭圆问题的新算法

基于有限元的渐近展开式,导出了新的外推公式,它们更精确地逼近密网上的有限元解(而不是微分方程的解).提出了新的外推瀑布型多网格法(EXCMG),采用新外推公式及其二次插值提供密网上的好初值.数值实验表明,新方法有很高的精度和效率.最后在PC机上求解了大规模二维椭圆问题.     

结合专业特色的理工科数学课程教学探讨

本文以湖南师范大学物理学专业数学物理方程的教学实践为基础,指出了目前理工科数学课程教学中存在的主要问题,探讨了高等院校数学教学与专业特色相结合的教学方法,并从教学内容、师资要求、教学方法和考核方式等方面提出某些具体改革措施,在教学实践中取得了初步成效．     

NEW ERROR EXPANSION FOR ONE-DIMENSIONAL FINITE ELEMENTS AND ULTRACONVERGENCE

Based on an improved orthogonal expansion in an element, a new error expression of n-degree finite element approximation uh to two-point boundary value problem is derived, and then supcrconvergence of two order for both function and derivatives are obtained.     

THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs

In this paper, we propose an accelerated search-extension method （ASEM） based on the interpolated coefficient finite element method, the search-extension method （SEM） and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in I-D and 2-D cases will show the efficiency of our approach.