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

WANG Cheng; HUANG Zi-ping; LI Li-kang

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(4): 477-482

WANG Cheng, HUANG Zi-ping, LI Li-kang. Two-Grid Partition of Unity Method for Second Order Elliptic Problems[J]. Applied Mathematics and Mechanics, 2008, 29(4): 477-482.

Citation:

WANG Cheng, HUANG Zi-ping, LI Li-kang. Two-Grid Partition of Unity Method for Second Order Elliptic Problems[J]. Applied Mathematics and Mechanics, 2008, 29(4): 477-482.

Citation:

WANG Cheng, HUANG Zi-ping, LI Li-kang. Two-Grid Partition of Unity Method for Second Order Elliptic Problems[J]. Applied Mathematics and Mechanics, 2008, 29(4): 477-482.

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

1.
Department of Mathematics, Tongji University, Shanghai 200092, P. R. China;

Received Date: 2007-10-03
Rev Recd Date: 2008-03-03
Publish Date: 2008-04-15

Abstract

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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References(11)

References

[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.