An a posteriori error estimator based on least-squares finite element solutions for viscoelastic fluid flows

Abstract

<p style='text-indent:20px;'>We present a posteriori error estimator strategies for the least-squares finite element method (LS) to approximate the exponential Phan-Thien-Tanner (PTT) viscoelastic fluid flows. The error estimator provides adaptive mass weights and mesh refinement criteria for improving LS solutions using lower-order basis functions and a small number of elements. We analyze an a priori error estimate for the first-order linearized LS system and show that the estimate is supported by numerical results. The LS approach is numerically tested for a convergence study and then applied to the flow past a slot channel. Numerical results verify that the proposed approach improves numerical solutions and resolves computational difficulties related to the presence of corner singularities and limitations arising from the exorbitant number of unknowns.</p>