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Piece-wise constant approximations in the membrane problem. (English) Zbl 1062.74561

Summary: 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.

MSC:

74K15 Membranes
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
65K10 Numerical optimization and variational techniques
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