On multigrid convergence in the indefinite case

Author:
R. A. Nicolaides

Journal:
Math. Comp. **32** (1978), 1082-1086

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1978-0520340-1

MathSciNet review:
0520340

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Abstract | References | Similar Articles | Additional Information

Abstract: Previous results of the author on the convergence of the multigrid method for positive definite elliptic problems are generalized to cover the indefinite case.

**[1]**Achi Brandt,*Multi-level adaptive solutions to boundary-value problems*, Math. Comp.**31**(1977), no. 138, 333–390. MR**0431719**, https://doi.org/10.1090/S0025-5718-1977-0431719-X**[2]**A. BRANDT,*Multi-level Adaptive Techniques*(*MLAT*):*Ideas and Software*, Proc. Conf. Math. Software, Math. Res. Center, Wisconsin, 1977.**[3]**RANDOLPH A. BANK & T. DUPONT,*An Optimal Order Process for Solving Elliptic Finite Element Equations*, Department of Mathematics, University of Chicago, 1978. (Manuscript.)**[4]**W. HACKBUSCH, "On the convergence of a multigrid iteration applied to finite element equations,"*Numer. Math.*(To appear.)**[5]**W. HACKBUSCH, "On the computation of eigenvalues and eigenfunctions of elliptic operator by means of a multigrid method,"*Numer. Math.*(To appear.)**[6]**W. HACKBUSCH,*A Fast Numerical Method for Elliptic Boundary Value Problems with Variable Coefficients*, 2nd GAMM Conference on Numer. Math. in Fluid Mechanics, DFVLR, Köln, October 1977.**[7]**R. A. NICOLAIDES,*On a Proposal for solving Discrete Finite Element Equations*, Proc. Conf. Linear Algebra and Finite Elements, Brunel University, June 1975.**[8]**R. A. Nicolaides,*On the 𝑙² convergence of an algorithm for solving finite element equations*, Math. Comp.**31**(1977), no. 140, 892–906. MR**0488722**, https://doi.org/10.1090/S0025-5718-1977-0488722-3**[9]**Gilbert Strang and George J. Fix,*An analysis of the finite element method*, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973. Prentice-Hall Series in Automatic Computation. MR**0443377**

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0520340-1

Article copyright:
© Copyright 1978
American Mathematical Society