Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates.

*(English)*Zbl 0567.65078This paper is concerned with a technique for implementing certain mixed finite elements based on the use of Lagrange multipliers to impose interelement continuity. The matrices arising from this implementation are positive definite. Considering some well-known mixed methods, namely the Raviart-Thomas methods for second order elliptic problems and the Hellan-Herrmann-Johnson method for biharmonic problems, the authors show that the computed Lagrange multipliers may be exploited in a simple postprocess to produce better approximation of the original variables. Moreover, an equivalence between the mixed methods and certain modified versions of nonconforming methods is considered.

Reviewer: J.Lovíšek

##### MSC:

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

65N15 | Error bounds for boundary value problems involving PDEs |

31A30 | Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions |

35J25 | Boundary value problems for second-order elliptic equations |

35J40 | Boundary value problems for higher-order elliptic equations |

##### Keywords:

nonconforming finite element methods; mixed finite elements; Lagrange multipliers; Raviart-Thomas methods; Hellan-Herrmann-Johnson method for biharmonic problems; Morley method
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\textit{D. N. Arnold} and \textit{F. Brezzi}, RAIRO, Modélisation Math. Anal. Numér. 19, 7--32 (1985; Zbl 0567.65078)

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