二阶椭圆问题带单位分解技巧的两重网格方法

王; 黄自萍; 李立康

二阶椭圆问题带单位分解技巧的两重网格方法

同济大学数学系,上海 200092;2.同济大学中德学院,上海 200092;3.复旦大学数学系,上海 200433

基金项目: 国家自然科学基金资助项目(40074031);上海市科学技术委员会基金资助项目

详细信息

作者简介:
王琤(1979- ),男,合肥人,博士生(E-mail:ewalexandre@hotmail.com);黄自萍,博士,教授,博士生导师(联系人.E-mail:huangziping@mail.tongji.edu.cn).

中图分类号: O242.21；O246
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出版历程
- 收稿日期: 2007-10-03
- 修回日期: 2008-03-03
- 刊出日期: 2008-04-15

Two-Grid Partition of Unity Method for Second Order Elliptic Problems

Department of Mathematics, Tongji University, Shanghai 200092, P. R. China;

摘要

摘要: 标准的两重网格方法是一种求解二阶椭圆问题的局部并行方法,其计算所得数值解在整个求解区域上并不连续．使用单位分解技术,将各个子区域上的局部解粘合在一起,从而得到全局连续解,并证明此解在H1范数意义下最优．更进一步,可以证明通过在粗网格上修正,能够改善其L2误差．数值例子验证了理论的正确性．
- 二阶椭圆问题 /
- 两重网格方法 /
- 单位分解
Abstract: A two-grid partition of unity method for second order elliptic problems was proposed and analyzed.The standard two-grid method is a local and parallel method which usually leads to a discontinuous solution in the whole computational domain.Partition of unity method was employed to glue all the local solutions together to get global continuous one,which is optimal in H1-norm.Furthermore,it is shown that the L2 error can be improved by using the coarse grid correction.Numerical experiments are reported to support the theory.
- second order elliptic problems /
- two-grid method /
- partition of unity

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参考文献(11)

[1]	Babuka I，Melenk J M.The partition of unity finite method[J].International Journal for Numerical Methods in Engineering,1997,40(4):727-758. doi: 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
[2]	Bank R E, Holst M J. A new paradigm for parallel adaptive meshing algorithms[J].SIAM Journal of Scientific Computing,2001,22(4):1411-1443.
[3]	HUANG Yun-qing,XU Jin-chao.A conforming finite element method for overlapping and nonmatching grids[J].Math Comp，2003,72(243):1057-1066.
[4]	Xu J C. A new class of iterative methods for nonself adjoint or indefinite problems[J].SIAM Journal on Numerical Analysis,1992,29(2):303-319. doi: 10.1137/0729020
[5]	Xu J C. Two-grid discretization techniques for linear and nonlinear PDEs[J].SIAM Journal on Numerical Analysis,1996,33(5):1759-1777. doi: 10.1137/S0036142992232949
[6]	Axelsson O,Layton W.A two-level discretization of nonlinear boundary value problems[J].SIAM Journal on Numerical Analysis,1996,33(6):2359-2374. doi: 10.1137/S0036142993247104
[7]	Dawson C N, Wheeler M F. Two-grid methods for mixed finite element approximations of nonlinear parabolic equations[J].Contemp Math,1994,180:191-203. doi: 10.1090/conm/180/01971
[8]	Dawson C N, Wheeler M F,Woodward C S. A two-grid finite difference scheme for nonliear parabolic equations[J].SIAM Journal on Numerical Analysis,1998,35(2):435-452. doi: 10.1137/S0036142995293493
[9]	Marion M, Xu J C. Error estimates on a new nonlinear Galerkin method based on two-grid finite elements[J].SIAM Journal on Numerical Analysis,1995,32(4):1170-1184. doi: 10.1137/0732054
[10]	Xu J C, Zhou A H. Local and parallel finite element algorithms based on two-grid discretizations[J].Mathematics of Computation,2000,69(231):881-909.
[11]	Ciarlet P G.The Finite Element Method for Elliptic Problems[M].Amsterdam:North-Holland,1978.

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二阶椭圆问题带单位分解技巧的两重网格方法

作者简介:
王琤(1979- ),男,合肥人,博士生(E-mail:ewalexandre@hotmail.com);黄自萍,博士,教授,博士生导师(联系人.E-mail:huangziping@mail.tongji.edu.cn).

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Two-Grid Partition of Unity Method for Second Order Elliptic Problems

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二阶椭圆问题带单位分解技巧的两重网格方法

作者简介: 王琤(1979- ),男,合肥人,博士生(E-mail:ewalexandre@hotmail.com);黄自萍,博士,教授,博士生导师(联系人.E-mail:huangziping@mail.tongji.edu.cn).

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出版历程

Two-Grid Partition of Unity Method for Second Order Elliptic Problems

计量

出版历程

目录

作者简介:
王琤(1979- ),男,合肥人,博士生(E-mail:ewalexandre@hotmail.com);黄自萍,博士,教授,博士生导师(联系人.E-mail:huangziping@mail.tongji.edu.cn).