FEM simulation of thixo-viscoplastic flow problems: error analysis

Abstract

This note is concerned with the essential part of Finite Element Methods (FEM) approximation of error analysis 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, nonoptimal estimate for microstructure, and extra regularity requirement for velocity, is due to the weak coercivity of microstructure operator on one hand and the modelling approach on the other hand, which we dealt with stabilized higher order FEM. Furthermore, we show the importance of taking into consideration the thixotropy inhabited in material by presenting the numerical solutions of TVP flow problems in a 4:1 contraction configuration.