A pressure-robust virtual element method for the Stokes problem

We present an arbitrary-order pressure-robust nonconforming virtual element method for the Stokes problem. Based on the local subtriangulations of polygons and the requirement of recovering the orthogonality between the velocity virtual space and the gradient forces, we introduce a computable reconstruction operator by modifying the classical Brezzi–Douglas–Marini interpolation operator. Under the shape regularity conditions, we show that the broken H 1 -semi-norm and L 2 -norm estimates of the velocity are independent of the pressure and the viscosity coefficient, and achieve the optimal convergence rates. Numerical results confirm the pressure-robust property and the uniform convergence of the method, especially when higher-order approximations are used.