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关于一个第二类变分不等式的有限元逼近 被引量:3

FINITE ELEMENT APPROXIMATION TO THE SECOND TYPE VARIATIONAL INEQUALITY
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摘要 1.引言本文讨论如下第二类变分不等式[1,2,3]的有限元逼近及其误差分析:求u∈V。 A new type of finite element scheme including the numerical integration modification is presented for the second type variational inequality. Our methods really simplify the finite element analysis and practical calculation. The unique existence and stability of finite element solution are proved , and particularly the optimal order error estimates are derived under H1 and L2 norms.
作者 张铁 李长军
出处 《计算数学》 CSCD 北大核心 2003年第3期257-264,共8页 Mathematica Numerica Sinica
基金 教育部高校骨干教师基金
关键词 第二类变分不等式 有限元逼近 误差分析 稳定性估计 数值积分修正格式 Second type variational inequality, finite element analy-sis, optimal L2 error estimate
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参考文献8

  • 1周天孝.利用依赖格网范数的有限元Lp误差估计[J].计算数学,1982,4(4):398-408.
  • 2周叔子.变分不等式及其有限元方法[M].长沙:湖南大学出版社,1994..
  • 3王烈衡.一个第二类变分不等式的有限元逼近[J].计算数学,2000,22(3):339-344. 被引量:2
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二级参考文献2

  • 1Xu J,Penn. State, Dept. Math. RepAM-48,1989年
  • 2周叔子,变分不等式及其有限元方法,1988年

共引文献2

同被引文献10

  • 1Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Amsterdam: North-Holand Publishing Company, 1978.
  • 2Glowinski R, Lions J L, Tremolieres R. Numerical Analysis of Variational Inequality[M]. Amsterdam:North-Holand Publishing Company, 1981.
  • 3沈树民.关于一类四阶变分不等式问题的C1—有限元方法[J].苏州大学学报(自然科学版),1988,10(2):149-155.
  • 4Glowinski R. Numerical Methods for Nonlinear Variational Problems[M]. New York: Springer-Verlag, 1984.
  • 5Stummel F. The generalized patch test[J]. SIAM J Numer Anal, 1979, 16(3): 449-471.
  • 6Duvant G, Lions J L. Les Inequations en Mecanique et en Physique[M]. Paris: Dunod, 1972.
  • 7Han W M, Wang L H. Nonconforming finite element analysis for a plate contact problem[J]. SIAM J Numer Anal, 2002, 40(5): 1683-1697.
  • 8Brenner S C, Scott L R. The Mathematical Theory of Finite Element Methods[M]. New York:Springer-Verlag, 1994.
  • 9QIAN Fu-bin,DING Rui.An FEM approximation for a fourth-order variational inequality of second kind[J].Applied Mathematics(A Journal of Chinese Universities),2008,23(1):19-24. 被引量:1
  • 10王烈衡.曲率障碍下一个四阶变分不等式的Morley元逼近[J].计算数学,1990,12(3):279-284. 被引量:9

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