Acta mathematica scientia, Series B >
L2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID (EXCMG)
Received date: 2008-09-01
Online published: 2009-05-20
Supported by
Supported by National Natural Science Foundation of China (10771063) and the Doctor Programme of the National Education Committee (20050542006)
Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method (EXCMG) is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.
Key words： cascadic multigrid; finite element; new extrapolation; ; quadratic interpolation; L2-error
CHEN Chuan-Miao , HU Hong-Ling , XIE Zi-Qing , LI Chen-Liang . L2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID (EXCMG)[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 539 -551 . DOI: 10.1016/S0252-9602(09)60052-7
[1] Brenner S, Scott L. The Mathematical Theory of Finite Element Methods. Berlin: Springer-Verlag, 1994
[2] Wang L H, Xu X J. Mathematical Foundations of Finite Element Methods. Beijing: Science Press, 2005
[3] Bornemann F, Deufhard P. The cascadic multigrid method for elliptic problems. Numer Math, 1996, 75: 125--152
[4] Shi Z C, Xu X J. Cascadic multigrid method for the second order elliptic problem. East-West J Numer Math, 1998, 6: 309--318; 1999, 7: 199--209
[5] Shi Z C, Xu X J. A new cascadic multigrid. Science in China Series A, 2001, 44(1): 21--30
[6] Shi Z C, Xu X J, Huang Y Q. Economical cascadic multigrid methods (ECMG). Science in China Series A, 2007, 50: 1765--1780
[7] Li C L, Chen C M, Xu X J. A cascadic mutligrid method based on superconvergence and extrapolation.
Numer Math Sinica, 2007, 29(4): 439--448
[8] Chen C M, Xie Z Q, Li C L, Hu H L. Study of a new extrapolation multigrid method (in English). Natur Sci J Hunan Normal Univ, 2007, 30(2): 1--5
[9] Chen C M, Hu H L, Xie Z Q, Li C L. Extrapolation cascadic multigrid method (EXCMG)--a new algorithm
in large scale solution of elliptic problems. Submitted to Numer Math Sinica \REF{
[10]} Chen C M, Hu H L, Xie Z Q, Li C L. Analysis of extrapolation cascadic multigrid method (EXCMG). Science in China Series A: athematics, 2008, 51(8): 1--12
[11] Marchuk G, Shaidurov V. Finite Difference and Their Extrapolations. Berlin: Springer-Verlag, 1983
[12] Chen C M. Superconvergence results in finite-element analysis. Surveys on Math for Industry, 2005, 11: 131--157
[13] Chen C M, Huang Y Q. High Accuracy Theory of Finite Elements. Changsha: Hunan Science and Technique Press, 1995
[14] Chen C M. Introduction to Scientific Computations. Beijing: Science Press, 2007
[15] Chen C M. Extrapolation of Galerkin solution. J Xiangtan Univ, 1980, 4: 1--6
[16] Chen C M, Huang Y Q. Extrapolation of triangular linear elements in general domain. Numer Math J Chinese Universities, 1989, 11: 1--16
[17] Chen C M, Lin Q. Extrapolation of finite element approximation in a rectangular domain. J Comput Math, 1989, 7: 227--233
[18] Lin Q, Yan N N. Structure and Analysis of Efficient Finite Elements. Baoding: Hebei University Press, 1996
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