Thesis Summary:

In this work, a posteriori error estimator applied to the problem of linearized elasticity is developed, theoretically and computationally. In the first place we propose the model problem, we introduce an auxiliary variable, the hydrostatic pressure, and we demonstrate the existence and uniqueness of the solution considering a mixed formulation of the problem, which allows us to consider both the case when the material is compressible and the incompressible . In the following chapter we demonstrate the existence and uniqueness of the discrete problem, considering the stabilized finite element method introduced by Franca and Stenberg and present an estimate of error a priori. Then, we perform the subsequent a posteriori error analysis using a residual type error estimator, demonstrating the equivalence between the estimator and the finite element error. Finally we present several numerical experiments that validate our error estimator a posteriori.