A Discontinuous Galerkin Method with Minimal Dissipation for a Finite-Strain Plate

Abstract

In this paper, we develop and analyze a discontinuous Galerkin (DG) method with minimal dissipation for the static bending problem of a finite-strain plate equation. The equations are deduced from a three-dimensional field equation. So the coupling of the equations and the mixed derivative terms are the barriers during developing discretization schemes. The error estimates of the scheme are proved in detail. Numerical experiments in different circumstances are presented to demonstrate the capabilities of the method.