Algebraic Analysis of the Hierarchical Basis Preconditioner

  • Authors:
  • Howard C. Elman;Xuejun Zhang

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 1995

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Abstract

The use of the hierarchical basis in finite element discretizations of two-dimensional elliptic partial differential equations produces matrices with condition numbers of order $O((\log h^{-1})^2)$. Standard proofs of this result are functional analytic in style. In this paper, it is shown that for uniform grids the result can be obtained using a purely linear algebraic argument.