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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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A quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem
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by Maurizio Paolini PDF
Math. Comp. 66 (1997), 45-67 Request permission


Solutions of the so-called prescribed curvature problem $\min _{A\subseteq \Omega } \mathcal {P}_ \Omega (A) - \int _A g(x)$, $g$ being the curvature field, are approximated via a singularly perturbed elliptic PDE of bistable type. For nondegenerate relative minimizers $A \subset \subset \Omega$ we prove an $\mathcal {O}( \epsilon ^2 |\log \epsilon |^2)$ error estimate (where $\epsilon$ stands for the perturbation parameter), and show that this estimate is quasi-optimal. The proof is based on the construction of accurate barriers suggested by formal asymptotics. This analysis is next extended to a finite element discretization of the PDE to prove the same error estimate for discrete minima.
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Additional Information
  • Maurizio Paolini
  • Affiliation: Dipartimento di Matematica e Informatica, Università di Udine, 33100, Udine, Italy
  • Email:
  • Received by editor(s): September 28, 1994
  • Received by editor(s) in revised form: August 9, 1995
  • Additional Notes: This work was partially supported by MURST (Progetto Nazionale “Equazioni di Evoluzione e Applicazioni Fisico-Matematiche” and “Analisi Numerica e Matematica Computazionale”) and CNR (IAN and Contracts 92.00833.01, 93.00564.01) of Italy.
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 45-67
  • MSC (1991): Primary 35B25, 35J60, 65N30; Secondary 35A35, 49Q05
  • DOI:
  • MathSciNet review: 1361810