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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.


Adaptive iterative linearization Galerkin methods for nonlinear problems
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by Pascal Heid and Thomas P. Wihler HTML | PDF
Math. Comp. 89 (2020), 2707-2734 Request permission


A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be obtained by applying a suitable preconditioning operator to the original (nonlinear) equation. Based on this observation, we will derive a unified abstract framework which recovers some prominent iterative schemes. In particular, for Lipschitz continuous and strongly monotone operators, we derive a general convergence analysis. Furthermore, in the context of numerical solution schemes for nonlinear partial differential equations, we propose a combination of the iterative linearization approach and the classical Galerkin discretization method, thereby giving rise to the so-called iterative linearization Galerkin (ILG) methodology. Moreover, still on an abstract level, based on two different elliptic reconstruction techniques, we derive a posteriori error estimates which separately take into account the discretization and linearization errors. Furthermore, we propose an adaptive algorithm, which provides an efficient interplay between these two effects. In addition, the ILG approach will be applied to the specific context of finite element discretizations of quasilinear elliptic equations, and some numerical experiments will be performed.
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Additional Information
  • Pascal Heid
  • Affiliation: Mathematics Institute, University of Bern, CH-3012 Switzerland
  • ORCID: 0000-0003-4227-4053
  • Email:
  • Thomas P. Wihler
  • Affiliation: Mathematics Institute, University of Bern, CH-3012 Switzerland
  • MR Author ID: 662940
  • ORCID: 0000-0003-1232-0637
  • Email:
  • Received by editor(s): August 15, 2018
  • Received by editor(s) in revised form: October 15, 2019
  • Published electronically: July 7, 2020
  • Additional Notes: The authors acknowledge the financial support of the Swiss National Science Foundation under grant no. 200021_182524
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 2707-2734
  • MSC (2010): Primary 47H10, 65N30; Secondary 47J25, 47H05, 49M15, 65J15
  • DOI:
  • MathSciNet review: 4136544