Hybridization and postprocessing in finite element exterior calculus

We hybridize the methods of finite element exterior calculus for Hodge–Laplace problem on differential k k -forms in alttext="double-struck upper R Superscript n"> R n encoding="application/x-tex">\mathbb {R}^n . In cases alttext="k equals 0"> = 0 encoding="application/x-tex">k=0 and encoding="application/x-tex">k=n , we recover well-known primal mixed hybrid scalar Poisson equation, while alttext="0 greater-than k > encoding="application/x-tex">0>k>n obtain new methods, including vector equation alttext="n 2"> 2 encoding="application/x-tex">n=2 3"> 3 encoding="application/x-tex">n=3 dimensions. also generalize Stenberg postprocessing [RAIRO Modél. Math. Anal. Numér. 25 (1991), pp. 151–167] from to arbitrary proving superconvergence estimates. Finally, discuss how this hybridization framework may be extended include nonconforming hybridizable discontinuous Galerkin methods.