A posteriori and a priori error estimates for linearized thin sheet folding

2025/07/01 by Antil, Harbir, Carney, Sean P., Khandelwal, Rohit
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2507.00807

Abstract

We describe a posteriori error analysis for a discontinuous Galerkin method for a fourth order elliptic interface problem that arises from a linearized model of thin sheet folding. The primary contribution is a local efficiency bound for an estimator that measures the extent to which the interface conditions along the fold are satisfied, which is accomplished by constructing a novel edge bubble function. We subsequently conduct a medius analysis to obtain improved a priori error estimates under the minimal regularity assumption on the exact solution. The performance of the method is illustrated by numerical experiments.

Citations

• Finite Element Methods for the Stretching and Bending of Thin Structures with Folding
• Γ-convergent LDG method for large bending deformations of bilayer plates
• Error Estimates For A Linear Folding Model
• Modeling and simulation of thin sheet folding
• Numerical analysis of the LDG method for large deformations of prestrained plates
• DG Approach to Large Bending Plate Deformations with Isometry Constraint
• Convergence of an adaptive C⁰-interior penalty Galerkin method for the biharmonic problem
• Bilayer Plates: Model Reduction, Γ-Convergent Finite Element Approximation and Discrete Gradient Flow
• Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity
• Babuška's paradox in a nonlinear bending-folding model

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