Direct computation of stresses in linear elasticity
This work provides a non-trivial generalization of a known method from 2D to 3D, offering a direct computation of stresses for elasticity problems.
The paper presents a new finite element method that directly approximates the strain tensor in linear elasticity, achieving optimal convergence rates. This extends a previous 2D method to 3D.
We present a new finite element method based on the formulation introduced by Philippe G.~Ciarlet and Patrick Ciarlet, Jr. in [{\em Math. Models Methods Appl. Sci., 15 (2005), pp. 259--571}], which approximates strain tensor directly. We also show the convergence rate of strain tensor is optimal. This work is a non-trivial generalization of its two dimensional analogue in [{\em Math. Models Methods Appl. Sci., 19 (2009), pp. 1043--1064}]