Approximation of a laminated microstructure for a rotationally invariant, double well energy density

Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We give error estimates for the approximation of a laminated microstructure which minimizes the energy ∫Ωφ(∇v(x))dx for a rotationally invariant, double well energy density φ(A). We present error estimates for the convergence of the deformation in L2, the convergence of directional derivatives of the deformation in the "twin planes," the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient.

Original languageEnglish (US)
Pages (from-to)205-221
Number of pages17
JournalNumerische Mathematik
Volume75
Issue number2
DOIs
StatePublished - Dec 1996

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