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

TL;DR

This paper develops a posteriori and a priori error estimates for a discontinuous Galerkin method applied to a fourth order elliptic interface problem modeling thin sheet folding, with novel efficiency bounds and numerical validation.

Contribution

It introduces a new local efficiency bound for error estimation using a novel edge bubble function and improves a priori error estimates with medius analysis.

Findings

Efficient error estimator for interface conditions

Improved a priori error bounds under minimal regularity

Numerical experiments confirm theoretical results

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.