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Summary: 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 body is almost incompressible. Several alternative a posteriori error estimators for the energy norm of the finite element error are introduced and analysed. We establish upper and lower bounds for the energy error in terms of these error estimators and show that the constants in the bounds are independent of the Lamé coefficients: The proposed estimators are robust in the incompressible limit. We also consider the requirement for pressure stabilisation when using lowest‐order conforming approximation. Computational results are presented that validate the theoretical estimates. The software used to generate these results is available online. [ABSTRACT FROM AUTHOR]

Modern software's allow computers to perform symbolic calculations in addition to simple numerical computations for which they were originally designed. This fact opens new possibilities in numerical simulation. In this paper a finite element implementation using the commercial software Wolfram Mathematica is used to solve a plane stress elasticity problem. The code adaptability from the provided examples to more challenging problems can easily be performed using the present code. Numerical examples with post‐processing illustrates the new tool and its flexibility. It has been proven in this study the feasibility of Wolfram Mathematica in learning and programming finite element methods for the solution of two‐dimensional problems in elasticity. [ABSTRACT FROM AUTHOR]