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Approximated convex envelope of a function. (English) Zbl 0796.65009
The problem is to analyze the efficiency of a \(P_ 1\)-finite element method to approximate some nonconvex energy function by a convex envelope. More precisely, the energy corresponding to a linear boundary deformation, the so-called “quasi-convexification of the energy density” must be minimized with help of this approximation. General convergence theorems are obtained for the triangular interpolation case and the one-dimensional case is studied in details.

MSC:
65D15 Algorithms for approximation of functions
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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