Network element methods for linear elasticity

Abstract

We explain how to derive a network element for the linear elasticity problem. After presenting sufficient conditions on the network for the validity of a discrete Korn inequality, we also propose several variations of the presented method and in particular we explain how it can be used on meshes to derive schemes that remain stable while keeping the stencil as compact as possible. Numerical examples illustrate the good behavior of the method, in both the mesh-based and truly meshless contexts.

Keywords

• Meshless methods
• Linear elasticity
• Variational methods