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Title: Numerical analysis of the LDG method for large deformations of prestrained plates
Abstract

A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in Bonito et al. (2022, LDG approximation of large deformations of prestrained plates. J. Comput. Phys., 448, 110719). This paper presents a numerical analysis of this LDG method, focusing on the free boundary case. The problem consists of minimizing a fourth-order bending energy subject to a nonlinear and nonconvex metric constraint. The energy is discretized using LDG and a discrete gradient flow is used for computing discrete minimizers. We first show $\varGamma $-convergence of the discrete energy to the continuous one. Then we prove that the discrete gradient flow decreases the energy at each step and computes discrete minimizers with control of the metric constraint defect. We also present a numerical scheme for initialization of the gradient flow and discuss the conditional stability of it.

 
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Award ID(s):
1817691 2110811
NSF-PAR ID:
10362345
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
IMA Journal of Numerical Analysis
Volume:
43
Issue:
2
ISSN:
0272-4979
Format(s):
Medium: X Size: p. 627-662
Size(s):
p. 627-662
Sponsoring Org:
National Science Foundation
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