HYBRIDIZATION AND POSTPROCESSING IN FINITE ELEMENT EXTERIOR CALCULUS

We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential k-forms in Rn. In the cases k = 0 and k = n, we recover well-known primal and mixed hybrid methods for the scalar Poisson equation, while for 0 < k < n, we obtain new hybrid finite element methods, including methods for the vector Poisson equation in n = 2 and n = 3 dimensions. We also generalize Stenberg postprocessing [RAIRO Mode ' l. Math. Anal. Nume ' r. 25 (1991), pp. 151-167] from k = n to arbitrary k, proving new superconvergence estimates. Finally, we discuss how this hybridization framework may be extended to include nonconforming and hybridizable discontinuous Galerkin methods.