Error Estimates For A Linear Folding Model

Abstract

An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical analysis of the discrete model includes an a priori error estimate in case of an accurate representation of the folding curve by the isoparametric mesh. Additional estimates show that geometric consistency errors may be controlled separately if the folding arc is approximated by piecewise polynomial curves. Various numerical experiments are carried out to validate the a priori error estimate for the folding model.

Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation

“…with the scaled bending energy t 2 E ben [y] := t 2 D 2 y 2 L 2 (Ω) , and realize that the meshsize parameter h plays a similar role to the thickness parameter t in the expansion of 1 t E 3D using (19) [16,23,25,24]. Moreover, allowing c r to vanish over a polygonal Γ made of edges of E h mimics discretely a material amenable to folding across Γ [53,54]. We prove convergence of minimizers of (68) with folding in our companion paper [45].…”