Numerical analysis of the LDG method for large deformations of prestrained plates Academic Article

abstract

• AbstractA 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.

authors

• Bonito, Andrea

published proceedings

• IMA JOURNAL OF NUMERICAL ANALYSIS

author list (cited authors)

• Bonito, A., Guignard, D., Nochetto, R. H., & Yang, S.

citation count

• 3

complete list of authors

• Bonito, Andrea||Guignard, Diane||Nochetto, Ricardo H||Yang, Shuo

publication date

• April 2023

publisher

• Oxford University Press (OUP)  Publisher

keywords

• Discrete Gradient Flow
• Free Boundary Conditions
• Local Discontinuous Galerkin
• Metric Constraint
• Prestrained Materials
• Reconstructed Hessian

Digital Object Identifier (DOI)

• 10.1093/imanum/drab103

start page

• 627

end page

• 662

volume

• 43

issue

• 2

URL

• http://dx.doi.org/10.1093/imanum/drab103