Stokes型积分-微分方程Q_2-P_1元的超收敛分析
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摘要
本文研究Q2-P1混合元对Stokes型积分-微分方程的有限元方法.利用积分恒等式技巧给出了关于流体速度u和压力p的误差估计,特别是在压力p的误差中去掉了影响解的稳定性的1因子t-2,改善了以往文献的结果.同时,通过构造适当的插值后处理算子得到了整体超收敛结果.
The Q2- P1 mixed finite element method is discussed for the Stokes type integro-differential equations. The error estimations of fluid velocity u and pressure p are given1 by the integral identity technique. Especially, in the estimation of pressure p the factor t-2which influences the stability of solution is removed and thus the existing results are improved accordingly. At the same time, the global superconvergence of order is derived based on the interpolation postprocessing approach.
The Q2- P1 mixed finite element method is discussed for the Stokes type integro-differential equations. The error estimations of fluid velocity u and pressure p are given1 by the integral identity technique. Especially, in the estimation of pressure p the factor t-2which influences the stability of solution is removed and thus the existing results are improved accordingly. At the same time, the global superconvergence of order is derived based on the interpolation postprocessing approach.
引文
[1]张铁.Stokes型积分-微分方程的Galerkin近似[J].高等学校计算数学学报,1997,(3):280–285.
[2]Girault V,Raviart P A.Finite method for Navier-Stokes equation,theory and algorithms[M].Berlin,Herdelberg:Springer-Verlag,1986.
[3]Temam R.Navier-Stokes equation,theory and numerical analysis[M].Amsterdam:North-Holland,1984.
[4]Brezzi F,Fortin M.Mixed and hybrid finite element methods[M].Berlin,Herdelberg:SpringerVerlag,1991.
[5]Crouzeix M,Raviart P A.Conforming and nonconforming finite dement methods for solving stationary Stokes equations[J].RAIRO Anal.Numer.,1973,7(3):33–75.
[6]王烈衡.Stokes问题的混合有限元分析[J].计算数学,1987,9(1):70–81.
[7]张铁.发展型积分-微分方程的有限元方法[M].沈阳:东北大学出版社,2001.
[8]石东洋,王培珍.各向异性网格下Stokes型积分-微分方程Beradi-Raugel混合元近似的超收敛分析[J].高等学校计算数学学报,2010,32(4):321–332.
[9]牛裕琪,石东洋.Stokes型积分-微分方程Bernadi-Raugel混合元的超收敛分析[J].河南师范大学学报,2011,39(4):6–9.
[10]石东洋,王培珍.Stokes型积分-微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法[J].高校应用数学学报,2009,24(4):435–442.
[11]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,2009,22(1):33–41.
[12]Lin Q,Lin J F.Finite element methods:accuracy and improvement[M].Beijing:Science Press,2006.
[13]Babuska I.The finite element methods with Lagrangian multipliners[J].Numer.Math.,1973,20(3):179–192.
[14]Brezzi F.On the existence,uniqueness and approximation of saddle-point problems arising from Lagrangian multipliners[J].RAIRO Anal.Numer.,1974,8(2):129–151.
[15]Girault V,Raviart P A.Finite element approximation of the Navier-Stokes equations[M].Lecture Notes in Math.,749,New York:Springer-Verlag,1979.
[16]石东洋,任金城.Stokes问题各向异性网格Q2-P1混合元超收敛分析[J].数学研究,2008,41(2):142–150.
[17]林群,严宁宁.高效有限元构造与分析[M].石家庄:河北大学出版社,1996:69–71.
[2]Girault V,Raviart P A.Finite method for Navier-Stokes equation,theory and algorithms[M].Berlin,Herdelberg:Springer-Verlag,1986.
[3]Temam R.Navier-Stokes equation,theory and numerical analysis[M].Amsterdam:North-Holland,1984.
[4]Brezzi F,Fortin M.Mixed and hybrid finite element methods[M].Berlin,Herdelberg:SpringerVerlag,1991.
[5]Crouzeix M,Raviart P A.Conforming and nonconforming finite dement methods for solving stationary Stokes equations[J].RAIRO Anal.Numer.,1973,7(3):33–75.
[6]王烈衡.Stokes问题的混合有限元分析[J].计算数学,1987,9(1):70–81.
[7]张铁.发展型积分-微分方程的有限元方法[M].沈阳:东北大学出版社,2001.
[8]石东洋,王培珍.各向异性网格下Stokes型积分-微分方程Beradi-Raugel混合元近似的超收敛分析[J].高等学校计算数学学报,2010,32(4):321–332.
[9]牛裕琪,石东洋.Stokes型积分-微分方程Bernadi-Raugel混合元的超收敛分析[J].河南师范大学学报,2011,39(4):6–9.
[10]石东洋,王培珍.Stokes型积分-微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法[J].高校应用数学学报,2009,24(4):435–442.
[11]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,2009,22(1):33–41.
[12]Lin Q,Lin J F.Finite element methods:accuracy and improvement[M].Beijing:Science Press,2006.
[13]Babuska I.The finite element methods with Lagrangian multipliners[J].Numer.Math.,1973,20(3):179–192.
[14]Brezzi F.On the existence,uniqueness and approximation of saddle-point problems arising from Lagrangian multipliners[J].RAIRO Anal.Numer.,1974,8(2):129–151.
[15]Girault V,Raviart P A.Finite element approximation of the Navier-Stokes equations[M].Lecture Notes in Math.,749,New York:Springer-Verlag,1979.
[16]石东洋,任金城.Stokes问题各向异性网格Q2-P1混合元超收敛分析[J].数学研究,2008,41(2):142–150.
[17]林群,严宁宁.高效有限元构造与分析[M].石家庄:河北大学出版社,1996:69–71.
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