Superconvergence and extrapolation for mixed finite element methods on rectangular domains

Wang, Jun Ping

doi:10.1090/S0025-5718-1991-1068807-0

Superconvergence and extrapolation for mixed finite element methods on rectangular domains
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Math. Comp. 56 (1991), 477-503 Request permission

Abstract:

Asymptotic expansions for the RT (Raviart-Thomas) mixed finite element approximation by the lowest-order rectangular element associated with a second-order elliptic equation on a rectangular domain are derived. Superconvergence for the vector field along the Gauss lines is obtained as a result of the expansion. A procedure of postprocessed extrapolation is presented for the scalar field, as well as procedures of pure Richardson extrapolation for both the vector and the scalar fields.

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