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Hybridization and postprocessing in finite element exterior calculus

08/01/2020
by   Gerard Awanou, et al.
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We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential k-forms in ℝ^n. 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 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.

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