Mixed Isogeometric Methods for Linear Elasticity with Weakly Imposed Symmetry

TL;DR

This paper develops and analyzes mixed isogeometric methods for linear elasticity problems with weak symmetry enforcement, enabling curved boundary modeling and providing theoretical and numerical validation.

Contribution

It introduces isogeometric discrete differential forms for weakly symmetric elasticity, extending existing methods to curved geometries with proven well-posedness and error estimates.

Findings

Method achieves stable discretization for curved domains.

Error estimates confirm convergence rates.

Numerical examples validate theoretical results.

Abstract

We consider and discretize a mixed formulation for linear elasticity with weakly imposed symmetry in two and three dimensions. Whereas existing methods mainly deal with simplicial or polygonal meshes, we take advantage of isogeometric analysis (IGA) and consequently allow for shapes with curved boundaries. To introduce the discrete spaces we use isogeometric discrete differential forms defined by proper B-spline spaces. For the proposed schemes a proof of well-posedness and an error estimate are given. Further we discuss our ansatz by means of different numerical examples.