Robust a posteriori error estimators for mixed approximation of nearly incompressible elasticity
For researchers in computational mechanics, this work provides robust error estimators that remain effective in the incompressible limit, addressing a known bottleneck in finite element analysis.
The paper proposes and analyzes robust a posteriori error estimators for mixed finite element approximations of nearly incompressible linear elasticity, proving that the estimators provide upper and lower bounds on the energy error with constants independent of the Lamé coefficients. Numerical results validate the theoretical estimates.
This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori error estimators for the energy norm of the finite element error are proposed and analysed. We establish upper and lower bounds for the energy error in terms of the proposed error estimators and prove that the constants in the bounds are independent of the Lamé coefficients: thus the proposed estimators are robust in the incompressible limit. Numerical results are presented that validate the theoretical estimates. The software used to generate these results is available online.