TY - JOUR
T1 - Analysis of a Second-Order Decoupled Time-Stepping Scheme for Transient Viscoelastic Flow
AU - Ravindran , S. S.
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 87
EP - 109
PY - 2020
DA - 2020/02
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13642.html
KW - Viscoelasticity, finite element method, discontinuous Galerkin method, decoupled scheme, error estimates, BDF2.
AB - <p style="text-align: justify;">In this paper, we propose and analyze a decoupled second order backward
difference formula (BDF2) time-stepping algorithm for solving transient viscoelastic fluid
flow. The spatial discretization is based on continuous Galerkin finite element approximation for the velocity and pressure, and discontinuous Galerkin finite element approximation
for the viscoelastic stress tensor. To obtain a non-iterative decoupled algorithm from the
fully discrete nonlinear system, we employ a second order extrapolation in time to the
nonlinear terms. The algorithm requires the solution of one Navier-Stokes problem and
one constitutive equation per time step. For mesh size $h$ and temporal step size ∆$t$ sufficiently small satisfying ∆$t$ ≤ $Ch$<sup>$d$</sup><sup>/4</sup>, a priori error estimates in terms of ∆$t$ and $h$ are
derived. Numerical tests are presented that illustrate the accuracy and stability of the
algorithm.</p>