Davini, Cesare Piece-wise constant approximations in the membrane problem. (English) Zbl 1062.74561 Meccanica 38, No. 5, 555-569 (2003). 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. Cited in 1 Document 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 Keywords:Numerical methods; Non-conforming approximations; G-convergence; Membranes PDFBibTeX XMLCite \textit{C. Davini}, Meccanica 38, No. 5, 555--569 (2003; Zbl 1062.74561) Full Text: DOI