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Interpolating minimal energy C 1 ‐Surfaces on P owell– S abin Triangulations: Application to the resolution of elliptic problems
Author(s) -
Fortes M. A.,
González P.,
Ibáñez M. J.,
Pasadas M.
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21918
Subject(s) - mathematics , domain (mathematical analysis) , bounded function , convergence (economics) , finite element method , resolution (logic) , quadratic equation , energy (signal processing) , space (punctuation) , surface (topology) , mathematical analysis , combinatorics , geometry , computer science , physics , statistics , artificial intelligence , economics , thermodynamics , economic growth , operating system
In this article, we present a method to obtain a C 1 ‐surface, defined on a bounded polygonal domain Ω, which interpolates a specific dataset and minimizes a certain “energy functional.” The minimization space chosen is the one associated to the Powell–Sabin finite element, whose elements are C 1 ‐quadratic splines. We develop a general theoretical framework for that, and we consider two main applications of the theory. For both of them, we give convergence results, and we present some numerical and graphical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 798–821, 2015