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Dual weighted a posteriori error estimation for a new nonconforming linear finite element on quadrilaterals. (English) Zbl 1074.65123

Summary: After a short introduction of a new nonconforming linear finite element on quadrilaterals recently developed by C. Park and D. Sheen [SIAM J. Numer. Anal. 41, No. 2, 624–640 (2003; Zbl 1048.65114)], we derive a dual weighted residual-based a posteriori error estimator (in the sense of R. Becker and R. Rannacher, East-West J. Numer. Math. 4, No. 4, 237–264 (1996; Zbl 0868.65076)) for this finite element. By computing a corresponding dual solution we estimate the error with respect to a given target error functional. The reliability and efficiency of this estimator is analyzed in several numerical experiments.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Software:

SPLIB; FEATFLOW
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Full Text: DOI

References:

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