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The Three-dimensional EQrot1 Non-conforming Finite Element

Author: LinFuBiao
Tutor: YangYiDu
School: Guizhou Normal
Course: Computational Mathematics
Keywords: the three-dimensional non-conforming EQ1rot element eigenvalue error eigenvalue lower bound extrapolation two-grid discretization schemes the three-dimensional non-conforming EQ1rot element two-grid discretization schemes igenvalue lower bounds
CLC: O241.82
Type: Master's thesis
Year: 2009
Downloads: 43
Quote: 0
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Abstract


The non-conforming EQ1rotelement was invented by Lin Q,Tobiska L,Zhou A in 2001.The type-function of corresponding finite element space keeps continuous under integral meaning when it overs single element boundary.The non-conforming character of the three-dimensional non-conforming EQ1rotelement in solving second-order elliptic boundary value problems and second-order elliptic equation problems is determined by the reduced continuity property.In two-dimensional case,Qun Lin and Jiafu Lin have studied the convergence and eigenvalue error expansion for the non-conforming EQ1rotelement,and They have proved that the non-conforming EQ1rotelement approximates eigenvalues from below on rectangular domains.In addition,in 2008,Yang Yidu et al proved the fact that the non-conforming EQ1rotelement approximates eigenvalues from below on polygonal domains that can be decomposed into rectangular elements.In three-dimensional case,because of the unknown number is 0(h-3)（h is the diameter of the mesh）,even if h is not sufficiently small,the amount of storage and calculation is very tremendous which is difficult to be accomplished in general computers.Say nothing of,the two-grid discretization schemes of finite element is applied to three-dimensional non-conforming EQ1rotelement,which is so called“three-dimensional trouble”.Therefore, there are very few papers about research of three-dimensional non-conforming EQ1rot element and few corresponding numerical experiments at present.However,in this paper,we prove that the compatible term error estimation and L2-norm error estimation for the three-dimensional non-conforming EQ1rotelement on the basis of paper.We prove that the eigenvalue error expansion for the three-dimensional non-conforming EQ1rotelement on the basis of paper.And further we easily obtain eigenvalue extrapolation algorithm（a posterior error estimate）for the three-dimensional non-conforming EQ1rotelement.We prove that the three-dimensional non-conforming EQ1rotelement approximates eigenvalues from below.We apply two-grid discretization schemes to the three-dimensional non-conforming EQ1rotelement on the basis of paper,we prove that finite element two-grid discretization schemes for the three-dimensional non-conforming EQ1rotelement approximates eigenvalues from below when exact eigenfunction is singular.Moreover,we give all the numerical examples.In addition,although the theoretical proof without being seen,the numerical experiments show that finite element two-grid discretization schemes for the three-dimensional non-conforming EQ1rotelement approximates eigenvalues from below when exact eigenfunction is not singular.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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