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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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Optimal-order error estimates for the finite element approximation of the solution of a nonconvex variational problem
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by Charles Collins and Mitchell Luskin PDF
Math. Comp. 57 (1991), 621-637 Request permission

Abstract:

Nonconvex variational problems arise in models for the equilibria of crystals and other ordered materials. The solution of these variational problems must be described in terms of a microstructure rather than in terms of a deformation. Moreover, the numerical approximation of the deformation gradient often does not converge strongly as the mesh is refined. Nevertheless, the probability distribution of the deformation gradients near each material point does converge. Recently we introduced a metric to analyze this convergence. In this paper, we give an optimal-order error estimate for the convergence of the deformation gradient in a norm which is stronger than the metric used earlier.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Math. Comp. 57 (1991), 621-637
  • MSC: Primary 65N15; Secondary 35J20, 35J70, 65N30, 73C99, 73V05
  • DOI: https://doi.org/10.1090/S0025-5718-1991-1094944-0
  • MathSciNet review: 1094944