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Superconvergence and extrapolation for mixed finite element methods on rectangular domains

Author: Jun Ping Wang
Journal: Math. Comp. 56 (1991), 477-503
MSC: Primary 65N30
MathSciNet review: 1068807
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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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Keywords: Second-order elliptic equation, finite element method, asymptotic expansion, superconvergence, Richardson extrapolation
Article copyright: © Copyright 1991 American Mathematical Society