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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.


Finite element approximation for the dynamics of asymmetric fluidic biomembranes
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by John W. Barrett, Harald Garcke and Robert Nürnberg PDF
Math. Comp. 86 (2017), 1037-1069 Request permission


We present a parametric finite element approximation of a fluidic membrane whose evolution is governed by a surface Navier–Stokes equation coupled to bulk Navier–Stokes equations. The elastic properties of the membrane are modelled with the help of curvature energies of Willmore and Helfrich type. Forces stemming from these energies act on the surface fluid, together with a forcing from the bulk fluid. Using ideas from PDE constrained optimization, a weak formulation is derived, which allows for a stable semi-discretization. An important new feature of the present work is that we are able to also deal with spontaneous curvature and an area difference elasticity contribution in the curvature energy. This allows for the modelling of asymmetric membranes, which compared to the symmetric case lead to quite different shapes. This is demonstrated in the numerical computations presented.
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Additional Information
  • John W. Barrett
  • Affiliation: Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdom
  • MR Author ID: 31635
  • Email:
  • Harald Garcke
  • Affiliation: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
  • MR Author ID: 352477
  • Email:
  • Robert Nürnberg
  • Affiliation: Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdom
  • MR Author ID: 698349
  • Email:
  • Received by editor(s): March 2, 2015
  • Received by editor(s) in revised form: October 13, 2015
  • Published electronically: August 18, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1037-1069
  • MSC (2010): Primary 65M60, 65M12, 76M10, 76Z99, 92C05, 35Q35, 76D05
  • DOI:
  • MathSciNet review: 3614011