Convex approximations of functionals with curvature
Giovanni Bellettini, Maurizio Paolini, Claudio Verdi (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
We address the numerical minimization of the functional , for . We note that can be equivalently minimized on the larger, convex, set and that, on that space, may be regularized with a sequence of regular functionals. Then both and can be discretized by continuous linear finite elements. The convexity of the functionals in is useful for the numerical minimization of . We prove the -convergence of the discrete functionals to and present a few numerical examples. ...