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

DOI:
https://doi.org/10.1090/S0025-5718-1991-1068807-0

MathSciNet review:
1068807

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1068807-0

Keywords:
Second-order elliptic equation,
finite element method,
asymptotic expansion,
superconvergence,
Richardson extrapolation

Article copyright:
© Copyright 1991
American Mathematical Society