非协调三维Morley元能量模的误差估计
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摘要
文给出了解决四阶椭圆边值问题非协调三维Morley元的构造,并且利用散度空间的性质,给出了三维非协调Morley元能量模的误差估计。本文所使用的方法与王明和徐进超的方法不一样,但所得到的收敛阶是一致的。
In this paper,a nonconforming 3D Morley element for fourth elliptic equations was given,and the error estimate of the energy norm for nonconforming 3D Morley element was obtained,according to the properties of the space related to divergence operator. The convergence order required is equal despite unlike Ming W and Xu J's method.
In this paper,a nonconforming 3D Morley element for fourth elliptic equations was given,and the error estimate of the energy norm for nonconforming 3D Morley element was obtained,according to the properties of the space related to divergence operator. The convergence order required is equal despite unlike Ming W and Xu J's method.
引文
[1]Lascaux P,Lesaint P.Some nonconforming finite elements for the plate bending problem[J].ESAIM:Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique,1975,9(R1):9-53.
[2]Arnold D N,Brezzi F.Mixed and conconforming finite element methods;implementation,postprocessing and error estimates[J].Modélisation mathématique et analyse numérique,1985,19(1):7-32.
[3]Ciarlet P G.The finite element method for elliptic problems[M].New York:Amsterdam,1978:256.
[4]石钟慈.关于Morley元的误差估计[J].计算数学,1990(2):113-118.
[5]陈绍春,石东洋.非协调板元的一般性误差估计式[J].计算数学,2000,22(3):295-300.
[6]Ming W,Xu J.Some tetrahedron nonconforming elements for fourth order elliptic equations[J].Math Comp,2007,25(4):408-420.
[7]Ruas,V.A quadratic finite element method for solving biharmonic problems in.Numer[J].Math,1988,52:33-43.
[8]Ming W,Xu J.The Morley element for fourth order elliptic equations in any dimensions[J].Numerische Mathematik,2006,103(1):155-169.
[9]Girault V,Raviart P A.Finite element approximation of the NavierStokes equations[M].Lecture Notes in Mathematics.Berlin:Springer Verlag,1979:749.
[10]Brenner S C,Scott R.The mathematical theory of finite element methods[M].New York:Springer,2010:371.
[2]Arnold D N,Brezzi F.Mixed and conconforming finite element methods;implementation,postprocessing and error estimates[J].Modélisation mathématique et analyse numérique,1985,19(1):7-32.
[3]Ciarlet P G.The finite element method for elliptic problems[M].New York:Amsterdam,1978:256.
[4]石钟慈.关于Morley元的误差估计[J].计算数学,1990(2):113-118.
[5]陈绍春,石东洋.非协调板元的一般性误差估计式[J].计算数学,2000,22(3):295-300.
[6]Ming W,Xu J.Some tetrahedron nonconforming elements for fourth order elliptic equations[J].Math Comp,2007,25(4):408-420.
[7]Ruas,V.A quadratic finite element method for solving biharmonic problems in.Numer[J].Math,1988,52:33-43.
[8]Ming W,Xu J.The Morley element for fourth order elliptic equations in any dimensions[J].Numerische Mathematik,2006,103(1):155-169.
[9]Girault V,Raviart P A.Finite element approximation of the NavierStokes equations[M].Lecture Notes in Mathematics.Berlin:Springer Verlag,1979:749.
[10]Brenner S C,Scott R.The mathematical theory of finite element methods[M].New York:Springer,2010:371.