非线性抛物方程的质量集中非协调元分析

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英文篇名：A Lumped Mass Nonconforming Finite Element Analysis for a Class of Nonlinear Parabolic Equations 作者：王琳 ; 石东伟 ; 石东洋 英文作者：WANG Lin~1,SHI Dong-wei~2,SHI Dong-yang~3 (1.Department of Basic Science,Henan Mechanical and Electrical Engineering College,Xinxiang 453000,China) (2.Department of Mathematics,Henan Institute of Science and Technology,Xinxiang 453000,China) (3.Department of Mathematics,Zhengzhou University,Zhengzhou 450052,China) 关键词：非线性抛物方程 ; 质量集中 ; Crank-Nicolson格式 ; 非协调元 ; 误差估计 英文关键词：nonlinear parabolic equations;;lumped mass;;Crank-Nicolson scheme;;nonconforming finite element;;error estimate 中文刊名：SSJS 英文刊名：Mathematics in Practice and Theory 机构：河南机电高等专科学校 基础部;河南科技学院 数学系;郑州大学 数学系; 出版日期：2013-01-23 出版单位：数学的实践与认识 年：2013 期：v.43 基金：国家自然科学基金(10671184,10971203);; 高等学校博士学科点专项基金(20094101110006) 语种：中文; 页：SSJS201302035 页数：8 CN：02 ISSN：11-2018/O1 分类号：240-247

摘要

将一个低阶Crouzeix-Raviart型非协调三角形元应用到一类非线性抛物方程,并建立了质量集中的半离散和向后Euler全离散逼近格式,在一般各向异性网格上利用插值算子导出了L~2-模的最优误差估计.
        A low order Crouzeix-Raviart type nonconforming triangular element is applied to a class of nonlinear parabolic equations in this paper,a lumped mass nonconforming finite element with Backward Euler approximation scheme is proposed,the L~2-norm error estimate is derived on the general anisotropic meshes by the finite element interpolation.

引文

[1]Nie Y Y,Thomee V.A lumped mass finite element method with quadrature for a nonlinear parabolic problem[J].IMA J Numer Anal,1985,(5):371-396.
    [2]Thomee V.Galerkin Finite Element Method for Parabolic Problems[M].New-York:Springer-Verlag, 1984.
    [3]黄明游.发展方程数值计算方法[M].北京:科学出版社,2004.
    [4]戴培良.Navier-Stokes方程的集中质量非协调有限元法[J].工程数学学报,2007,24(2):249-253.
    [5]Zhang T,Lin Y P.A lumped mass finite element method for nonlinear parabolic integro-differential equations[J].Numer Math J Chinese University,1997,6(3):281-285.
    [6]石东洋,王慧敏.Stokes型积分微分方程的质量集中各向异性非协调有限元分析[J].应用数学,2009,(1): 33-41.
    [7]石东洋,王慧敏.非定常Navier-Stokes方程的质量集中各向异性非协调有限元逼近[J].数学物理学报, 2010,(4):1018-1029.
    [8]石东洋,谢萍丽.Sobolev方程的一类各向异性非协调有限元逼近[J].系统科学与数学,2009,29(1): 116-128.
    [9]Shi D Y,Wang H H,Du Y P.Anisotropic nonconforming finite element method approximating a class of nonlinear Sobolev equations[J].J Comput Math,2009,27(2-3):299-314.
    [10]Shi D Y,Pei L F.Low order Crouzeix-Raviart type nonconforming finite element methods for approximating Maxwell equations[J].Int J Numer Anal Model,2008,5(3):373-385.
    [11]Shi D Y,Ren J C.Nonconforming mixed finite element method for the stationary conduction convection problem[J].Int.J.Numer.Anal.Model,2009,6(2):293-310.
    [12]Shi D Y,Wang C X.A new low order nonconforming mixed finite element scheme for second order elliptic problems[J].Int J of Comput Math,2011,88(10):2167-2177.
    [13]Shi D Y,Ren J C,W.Gong.A new nonconforming mixed finite element scheme for the stationary Navier-Stokes equations[J].Acta Math Scientia,2011,31(2):367-382.
    [14]马戈,石东洋.广义神经传播方程的非协调混合有限元方法[J].数学的实践与认识,2010(04):217-223.
    [15]吴志勤,王芬玲,石东洋.广义神经传播方程的一个新的超收敛估计及外推[J].数学的实践与认识, 2011(15):234-240.
    [16]Shi D Y,Xu C.An anisotropic locking-free nonconforming triangular finite element method for planar linear elasticity problem[J].J Comput Math,2012,30(2):124-138.
    [17]Shi D Y,Xu C.Anisotropic nonconforming Crouzeix-Raviart type FEM for second order elliptic prdblem[J].Appl Math Mech,2012,33(2):243-252.