Comparison of a Finite Element Method and a Finite Volume Method for Flow on General Grids in 3D

We compare the recently developed Vertex Approximate Gradient (VAG) scheme developed in [R. Eymard et al., ESAIM: Mathematical Modelling and Numerical Analysis, 46(2), 2012] and the multipoint flux approximations (MPFA) O- and L-methods on 3D irregular meshes. It is found that the VAG scheme converges for a wider range of problems than the MPFA methods, however when the MPFA-methods converge, the convergence rate in flux is better than for the VAG method.