We present a technique for the approximation of quadratic variational problems of the first order in spaces of piece-wise constant functions. The method adopts ideas from the theory of $\Gamma$-convergence as a guideline, and it differs from more traditional non-conforming techniques because it is based on the introduction of a suitable sequence of discrete functionals to be minimized with no constraints and without requiring that the spline functions fulfill any patch test condition.
Piece-wise Constant Approximations in the Membrane Problem
DAVINI, Cesare
2003-01-01
Abstract
We present a technique for the approximation of quadratic variational problems of the first order in spaces of piece-wise constant functions. The method adopts ideas from the theory of $\Gamma$-convergence as a guideline, and it differs from more traditional non-conforming techniques because it is based on the introduction of a suitable sequence of discrete functionals to be minimized with no constraints and without requiring that the spline functions fulfill any patch test condition.File in questo prodotto:
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