Divergence-conforming HDG methods for Stokes flows

Source abstract

In this paper, we show that by sending the normal stabilization function to infinity in the hybridizable discontinuous Galerkin methods previously proposed in [Comput. Methods Appl. Mech. Engrg. 199 (2010), 582–597], for Stokes flows, a new class of divergence-conforming methods is obtained which maintains the convergence properties of the original methods. Thus, all the components of the approximate solution, which use polynomial spaces of degree k k , converge with the optimal order of k + 1 k+1 in L 2 L^2 for any k ≥ 0 k \ge 0 . Moreover, the postprocessed velocity approximation is also divergence-conforming, exactly divergence-free and converges with order k + 2 k+2 for k ≥ 1 k\ge 1 and with order 1 1 for k = 0 k=0 . The novelty of the analysis is that it proceeds by taking the limit when the normal stabilization goes to infinity in the error estimates recently obtained in [Math. Comp., 80 (2011) 723–760].