A Priori and a Posteriori Error Analysis of TDNNS Method for Linear Elasticity Problem Under Minimal Regularity

In this paper, a priori and a posteriori error estimates of the tangential-displacement normal-normal-stress (TDNNS) method for linear elasticity problem with strongly symmetric stress tensors are proposed. The error estimator is established by decomposing the stress error into two components via the introduction of an auxiliary problem. The local efficiency of the error estimator is proved via bubble function techniques. Then, we derive a priori error estimates under minimal regularity. Classical methodologies rely on Galerkin orthogonality, which hinges on the well-defined trace variables on the inter-element boundaries. In order to circumvent the Galerkin orthogonality, an alternative methodology in the spirit of the medius analysis is established to prove the convergence error estimates for L² -error of stress, mesh-dependent energy error of displacement and L² -error of displacement. Several numerical experiments are presented to verify the performances of the proposed error estimator and confirm the convergence error estimates of the method especially for problems with low regularity. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.