A Priori Error Analysis and Finite Element Approximations for a Coupled Model Under Nonlinear Slip Boundary Conditions
摘要
We consider the time-dependent Navier–Stokes system coupled with the heat equation governed by the nonlinear Tresca boundary conditions. We propose a discretization of these equations that combines Euler implicit scheme in time and finite element approximations in space. We present optimal error estimates for velocity, pressure and temperature. Numerical examples are displayed to illustrate the theoretical results.