Numerische Mathematik

, Volume 52, Issue 4, pp 427–458

The hierarchical basis multigrid method

  • Randolph E. Bank
  • Todd F. Dupont
  • Harry Yserentant

DOI: 10.1007/BF01462238

Cite this article as:
Bank, R.E., Dupont, T.F. & Yserentant, H. Numer. Math. (1988) 52: 427. doi:10.1007/BF01462238


We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß-Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigridV-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes.

Subject Classifications

AMS(MOS): 65F1065F3565N2065N30CR:G1.8

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Randolph E. Bank
    • 1
  • Todd F. Dupont
    • 2
  • Harry Yserentant
    • 3
  1. 1.Department of MathematicsUniversity of California at San DiegoLa JollaUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA
  3. 3.Fachbereich MathematikUniversität DortmundDortmund 50Federal Republic of Germany