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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.


An optimal adaptive Fictitious Domain Method
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by Stefano Berrone, Andrea Bonito, Rob Stevenson and Marco Verani HTML | PDF
Math. Comp. 88 (2019), 2101-2134 Request permission


We consider a fictitious domain formulation of an elliptic partial differential equation and approximate the resulting saddle-point system using a nested inexact preconditioned Uzawa iterative algorithm, which consists of three nested loops. In the outer loop the trial space for the Galerkin approximation of the Lagrange multiplier is enlarged. The intermediate loop solves this Galerkin system by a damped preconditioned Richardson iteration. Each iteration of the latter involves solving an elliptic problem on the fictitious domain whose solution is approximated by an adaptive finite element method in the inner loop. We prove that the overall method converges with the best possible rate and illustrate numerically our theoretical findings.
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Additional Information
  • Stefano Berrone
  • Affiliation: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
  • MR Author ID: 679290
  • Email:
  • Andrea Bonito
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 783728
  • Email:
  • Rob Stevenson
  • Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
  • MR Author ID: 310898
  • Email:
  • Marco Verani
  • Affiliation: MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo Da Vinci, 32, 20133 Milano, Italy
  • MR Author ID: 704488
  • Email:
  • Received by editor(s): December 26, 2017
  • Received by editor(s) in revised form: September 2, 2018, and November 2, 2018
  • Published electronically: February 22, 2019
  • Additional Notes: The first author was partially supported by INdAM-GNCS and
    The second author was partially supported by NSF Grant DMS-1254618.
    The fourth author was partially supported by INdAM-GNCS
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2101-2134
  • MSC (2010): Primary 41A25, 42C40, 65N12, 65T60, 65M85, 65N30
  • DOI:
  • MathSciNet review: 3957888