Volume 15, Number 2, April-June 2009
|Page(s)||322 - 366|
|Published online||24 June 2008|
The regularisation of the N-well problem by finite elements and by singular perturbation are scaling equivalent in two dimensions
MIS MPG, Inselstrasse 22,
04103 Leipzig, Germany. email@example.com
Revised: 15 January 2008
Let where are matrices of non-zero determinant. We establish a sharp relation between the following two minimisation problems in two dimensions. Firstly the N-well problem with surface energy. Let , be a convex polytopal region. Define and let AF denote the subspace of functions in that satisfy the affine boundary condition Du=F on (in the sense of trace), where . We consider the scaling (with respect to ϵ) of Secondly the finite element approximation to the N-well problem without surface energy. We will show there exists a space of functions where each function is piecewise affine on a regular (non-degenerate) h-triangulation and satisfies the affine boundary condition v=lF on (where lF is affine with ) such that for there exists positive constants (depending on , p) for which the following holds true
Mathematics Subject Classification: 74N15
Key words: Two wells / surface energy
© EDP Sciences, SMAI, 2008
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