An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, p. 921-934

In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.

Classification:  74B20,  74S05
Keywords: finite-well non-convex functionals, finite element approximations
@article{M2AN_2001__35_5_921_0,
     author = {Lorent, Andrew},
     title = {An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     pages = {921-934},
     zbl = {1017.74067},
     mrnumber = {1866275},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_5_921_0}
}
Lorent, Andrew. An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, pp. 921-934. http://www.numdam.org/item/M2AN_2001__35_5_921_0/

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