|
A two-grid discretization scheme for eigenvalue problems
Author(s):
Jinchao
Xu;
Aihui
Zhou.
Journal:
Math. Comp.
70
(2001),
17-25.
MSC (2000):
Primary 65L15, 65N15, 65N25, 65N30, 65N55
Posted:
August 17, 1999
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
A two-grid discretization scheme is proposed for solving eigenvalue problems, including both partial differential equations and integral equations. With this new scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid, and the solution of a linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy.
References:
- 1.
- Adams R.A.(1975): Sobolev Spaces, Academic Press, New York. MR 56:9247
- 2.
- Axelsson, O. and Layton, W.(1996): A two-level discretization of nonlinear boundary value problems, SIAM J. Numer. Anal., 33, 2359-2374. MR 98c:65181
- 3.
- Babuska, I. and Osborn, J.E.(1989): Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems, Math. Comp., 52, 275-297. MR 89k:65132
- 4.
- Babuska, I. and Osborn, J.E.(1991): Eigenvalue problems, Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part 1) (P.G. Ciarlet and J.L. Lions, eds.), Elsevier, 641-792. MR 92f:65001
- 5.
- Chatelin, F.(1983): Spectral Approximations of Linear Operators, Academic Press, New York. MR 86d:65071
- 6.
- Ciarlet, P.G. and Lions J.L.(1991): Handbook of Numerical Analysis, Vol.II, Finite Element Methods (Part I), North-Holland. MR 92f:65001
- 7.
- Dawson, C.N. and Wheeler, M.F.(1994): Two-grid methods for mixed finite element approximations of nonlinear parabolic equations, Contemp. Math., 180, 191-203. MR 95j:65117
- 8.
- Dawson, C.N., Wheeler, M.F. and Woodward, C.S.(1998): A two-grid finite difference scheme for nonlinear parabolic equations, SIAM J. Numer. Anal.,35, 435-452. MR 99b:65097
- 9.
- Layton, W. and Lenferink, W.(1995): Two-level Picard and modified Picard methods for the Navier-Stokes equations, Appl. Math. Comp., 69, 263-274. MR 95m:65191
- 10.
- Lin, Q.(1979): Some problems concerning approximate solutions of operator equations, Acta Math. Sinica, 22, 219-230(Chinese). MR 80k:65056
- 11.
- Marion, M. and Xu, J.(1995): Error estimates on a new nonlinear Galerkin method based on two-grid finite elements, SIAM J. Numer. Anal., 32, 1170-1184. MR 96f:65136
- 12.
- Utnes, T.(1997): Two-grid finite element formulations of the incompressible Navier-Stokes equations, Comm. Numer. Methods Engrg., 34, 675-684. MR 98d:76110
- 13.
- Xu, J.(1992): A new class of iterative methods for nonselfadjoint or indefinite problems, SIAM J. Numer. Anal., 29, 303-319. MR 92k:65063
- 14.
- Xu, J.(1992): Iterative methods by space decomposition and subspace correction, SIAM Review, 34, 4, 581-613. MR 93k:65029
- 15.
- Xu, J.(1994): A novel two-grid method for semilinear equations, SIAM J. Sci. Comput., 15, 231-237. MR 94m:65178
- 16.
- Xu, J.(1996): Two-grid discretization techniques for linear and nonlinear PDEs, SIAM J. Numer. Anal., 33, 1759-1777. MR 97i:65169
- 17.
- Xu, J. and Zhou, A.(1998): Local and parallel finite element algorithms based on two-grid discretizations, Math. Comp.(to appear).
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(2000):
65L15, 65N15, 65N25, 65N30, 65N55
Retrieve articles in all Journals with MSC
(2000):
65L15, 65N15, 65N25, 65N30, 65N55
Additional Information:
Jinchao
Xu
Affiliation:
Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email:
xu@math.psu.edu
Aihui
Zhou
Affiliation:
Institute of Systems Science, Academia Sinica, Beijing 100080, China
Email:
azhou@bamboo.iss.ac.cn
DOI:
10.1090/S0025-5718-99-01180-1
PII:
S 0025-5718(99)01180-1
Keywords:
Eigenvalue problems,
finite elements,
partial differential equations,
integral equations,
two-grid method
Received by editor(s):
December 16, 1998
Received by editor(s) in revised form:
February 25, 1999
Posted:
August 17, 1999
Additional Notes:
This work was partially supported by NSF DMS-9706949, NSF ACI-9800244 and NASA NAG2-1236 through Penn State, and the Center for Computational Mathematics and Applications, The Pennsylvania State University, and by NSF ASC 9720257 through UCLA. The second author was also partially supported by National Science Foundation of China.
Copyright of article:
Copyright
1999,
American Mathematical Society
|
Comments: webmaster@ams.org