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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Inverse-type estimates on $hp$-finite element spaces and applications
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by Emmanuil H. Georgoulis PDF
Math. Comp. 77 (2008), 201-219 Request permission


This work is concerned with the development of inverse-type inequalities for piecewise polynomial functions and, in particular, functions belonging to $hp$-finite element spaces. The cases of positive and negative Sobolev norms are considered for both continuous and discontinuous finite element functions.The inequalities are explicit both in the local polynomial degree and the local mesh size.The assumptions on the $hp$-finite element spaces are very weak, allowing anisotropic (shape-irregular) elements and varying polynomial degree across elements. Finally, the new inverse-type inequalities are used to derive bounds for the condition number of symmetric stiffness matrices of $hp$-boundary element method discretisations of integral equations, with element-wise discontinuous basis functions constructed via scaled tensor products of Legendre polynomials.
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Additional Information
  • Emmanuil H. Georgoulis
  • Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom
  • Email:
  • Received by editor(s): February 27, 2006
  • Received by editor(s) in revised form: December 4, 2006
  • Published electronically: September 18, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 201-219
  • MSC (2000): Primary 65J05; Secondary 65R20
  • DOI:
  • MathSciNet review: 2353949