An extended family of nonconforming quasi-Wilson elements for solving elasticity problem

摘要

This contribution (part two) focuses on numerical implementation and efficiency aspects of an extended family of nonconforming quasi-Wilson elements type. Such a class of nonconforming elements has been introduced recently in Achchab et al. (2015). Here, based on a rectangular mesh, it is used for the approximate solution of a planar elasticity problem. It is shown that this family passes the patch-test, and that by suitably adding some orthogonality conditions, on a general class of enrichment functions, we can derive higher order consistency error estimates. Our general theoretical results, see Theorems 4.1 and 4.2, unify, simplify and extend a number of existing works on the improvement of the order of consistency error. Numerical experiments are carried out to demonstrate that our method is optimal for various Lamé parameter μ, shear modulus λ and locking free when the Poisson parameter ν approaches close to 0.5.