Numerical assessment of pressure, velocity, and stress post-processing strate- gies for the Biot’s problem

Resumo

In the context of the displacement-pressure formulation for the Biot’s problem, the present work ex-plores some possibilities of Finite Element post-processings to improve the accuracy of the pressure field, the Darcy velocity, and the effective stress. Numerical experiments illustrate the performance of the different strategies and compare their results with the native approximations obtained through the use of the lowest-order Taylor-Hood space in the displacement-pressure Galerkin method. Our results indicate that the post-processing strategies pre- sented significantly improve the approximation of the velocity and effective stress fields. The pressure field, on the other hand, does not benefit as much from the strategies considered here.