FEM simulation of thixo-viscoplastic flow problems: Error analysis

Abstract

This note is concerned with error analysis of FEM approximations for quasi-Newtonian modelling of thixo-viscoplastic, TVP, flow problems. The developed FEM settings for thixotropic generalized Navier-Stokes equations is based on a constrained monotonicity and continuity for the coupled system, which is a cornerstone for an efficient monolithic Newton-multigrid solver. The manifested coarseness in the energy inequality by means of proportional dependency of its constants on regularization parameter, nonoptimal estimate for microstructure, and extra regularization requirement for velocity, is due to weak coercivity of microstructure operator on one hand and the modelling approach on the other hand, which we dealt with higher order stabilized FEM. Furthermore, we showed the importance of taking into consideration the thixotropy inhabited in material by presenting the numerical simulations of TVP flow problems in a 4:1 contraction configuration.