Preconditioning and Two-Level Multigrid Methods of Arbitrary Degree of Approximation By

  title={Preconditioning and Two-Level Multigrid Methods of Arbitrary Degree of Approximation By},
  author={Owe Axelsson and Ivar Gustafsson},
Let A be a mesh parameter corresponding to a finite element mesh for an elliptic problem. We describe preconditioning methods for two-level meshes which, for most problems solved in practice, behave as methods of optimal order in both storage and computational complexity. Namely, per mesh point, these numbers are bounded above by relatively small constants for all h > h0, where h0 is small enough to cover all but excessively fine meshes. We note that, in practice, multigrid methods are actually… CONTINUE READING
Highly Influential
This paper has highly influenced 11 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 101 citations. REVIEW CITATIONS


Publications citing this paper.
Showing 1-10 of 31 extracted citations

On parallel solution of linear elasticity problems. Part III: higher order finite elements

Numerical Lin. Alg. with Applic. • 2013
View 9 Excerpts
Method Support
Highly Influenced

Robust algebraic multilevel preconditioning in H(curl) and H(div)

Computers & Mathematics with Applications • 2013
View 4 Excerpts
Highly Influenced

An efficient hierarchical preconditioner for quadratic discretizations of finite element problems

Numerical Lin. Alg. with Applic. • 2011
View 5 Excerpts
Method Support
Highly Influenced


View 5 Excerpts
Method Support
Highly Influenced

102 Citations

Citations per Year
Semantic Scholar estimates that this publication has 102 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-9 of 9 references

Analysis of a Two-Level Scheme for Solving Finite Element Equations, Report CNA-159, Center for Numerical Analysis, The University of Texas

R. Bank, T. Dupont
View 5 Excerpts
Highly Influenced

Introduction to multigrid methods," Colloquium Numerical Solution of Partial Differential Equations

P. W. Hemker
(J. G. Verwer, ed.), MC SYLLABUS 44, Mathematisch Centrum, Amsterdam, • 1980
View 2 Excerpts

Stability and Rate of Convergence of Modified Incomplete Cholesky Factorization Methods, Thesis, Report 79.02R

I. Gustafsson
View 2 Excerpts

The incomplete Cholesky conjugate gradient method for the iterative solution of systems of linear equations,

D. Kershaw
J. Comput. Phys., v • 1978
View 1 Excerpt

A class of iterative methods for finite element equations," Comput

O. Axelsson
Methods Appl. Mech. Engrg., v • 1976

Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition numbers,"

I. Fried
Sound Vibration, v • 1972