The discrete duality finite volume method for Stokes equations on three-dimensional polyhedral meshes

We develop a discrete duality finite volume method for the three-dimensional steady Stokes problem with a variable viscosity coefficient on polyhedral meshes. Under very general assumptions on the mesh, which may admit nonconforming polyhedrons, we prove the stability and well-posedness of the scheme. We also prove the convergence of the numerical approximation to the velocity, velocity gradient, and pressure and derive a priori estimates for the corresponding approximation error. Final numerical experiments confirm the theoretical predictions.