摘要
By the standard theory,the stable Qk+1,k−Qk,k+1/Qdck divergence-free element converges with the optimal order of approximation for the Stokes equations,but only order k for the velocity in H1-norm and the pressure in L2-norm.This is due to one polynomial degree less in y direction for the first component of velocity,which is a Qk+1,k polynomial of x and y.In this manuscript,we will show by supercloseness of the divergence free element that the order of convergence is truly k+1,for both velocity and pressure.For special solutions(if the interpolation is also divergence-free),a two-order supercloseness is shown to exist.Numerical tests are provided confirming the accuracy of the theory.
