Superconvergence of finite element discretization of time relaxation models of advection
The nodal accuracy of finite element discretizations of advection equations including a time relaxation term is studied. Worst case error estimates have been proven for this combination (for the Navier-Stokes equations) by energy methods. By considering the Cauchy problem with uniform meshes, precise Fourier analysis of the error is possible. This analysis shows (1) the worst case upper bounds are sharp in the meshwidth h, (2) time relaxation stabilization does not degrade superconvergence of the usual FEM, (3) time relaxation itself is possibly superconvergent and (4) higher order time relaxation is preferable to maintain small numerical errors.
superconvergence time relaxation deconvolution