Stress recovery for the polygonal finite element method

The finite element method is one of the most used numerical tools for engineering design. In recent years, novel numerical approximations have been proposed to extend the finite element method to meshes using arbitrary polygons. Such approximations are aimed to improve accuracy and increase the flexibility during the meshing process. However, as any approximation, they exhibit an error that requires to be quantified in order to validate the numerical results. In this paper, we present a technique to estimate the discretization error in energy norm for arbitrary polygonal finite element meshes. This recovery-based technique uses a moving least squares approach that considers constraints to represent the equilibrium equations. We use two benchmark problems to evaluate the effectivity of the error estimator, with good results both locally and globally.