Finite difference/element method for time-fractional Navier-Stokes equations
This work provides a numerical framework for solving fractional Navier-Stokes equations, which is of interest to researchers in computational fluid dynamics and fractional calculus.
The authors developed a combined finite difference and finite element method for solving time-fractional Navier-Stokes equations, proving stability and convergence error estimates, and validating with a numerical example.
We apply a composite idea of semi-discrete finite difference approximation in time and Galerkin finite element method in space to solve the Navier-Stokes equations with Caputo derivative of order 0 < α < 1. The stability properties and convergence error estimates for both the semi-discrete and fully discrete schemes are obtained. Numerical example is provided to illustrate the validity of theoretical results.