A weak Galerkin method for the nonlinear Navier–Stokes problem

In this paper, we introduce a weak Galerkin method for the nonlinear Navier–Stokes problem. To obtain the approximation of the velocity, we use the combination of piecewise linear polynomials on the elements and piecewise constants on the edges. For the approximation of the pressure, we use the piecewise constants on the elements. With proper regularity assumptions, we derive the error estimates for the velocity in the energy norm and the pressure in the \(L^{2}\) $L^2$ norm. Finally, we provide several numerical examples to support the theoretical conclusions.