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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Inf-sup stability implies quasi-orthogonality
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by Michael Feischl HTML | PDF
Math. Comp. 91 (2022), 2059-2094 Request permission


We prove new optimality results for adaptive mesh refinement algorithms for non-symmetric, indefinite, and time-dependent problems by proposing a generalization of quasi-orthogonality which follows directly from the inf-sup stability of the underlying problem. This completely removes a central technical difficulty in modern proofs of optimal convergence of adaptive mesh refinement algorithms and leads to simple optimality proofs for the Taylor-Hood discretization of the stationary Stokes problem, a finite-element/boundary-element discretization of an unbounded transmission problem, and an adaptive time-stepping scheme for parabolic equations. The main technical tools are new stability bounds for the $LU$-factorization of matrices together with a recently established connection between quasi-orthogonality and matrix factorization.
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Additional Information
  • Michael Feischl
  • Affiliation: Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna
  • MR Author ID: 965785
  • Email:
  • Received by editor(s): July 15, 2021
  • Received by editor(s) in revised form: January 1, 2022, and March 2, 2022
  • Published electronically: July 8, 2022
  • Additional Notes: This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 258734477 – SFB 1173 as well as the Austrian Science Fund (FWF) under the special research program Taming complexity in PDE systems (grant SFB F65)
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2059-2094
  • MSC (2020): Primary 65N30, 65N50, 15A23
  • DOI:
  • MathSciNet review: 4451456