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      Raviart Thomas Petrov-Galerkin Finite Elements

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          Abstract

          The general theory of Babu\v{s}ka ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard. Moreover, the mixed method of Raviart-Thomas with low-level elements can be interpreted as a finite volume method with a non-local gradient. In this contribution, we propose a variant of type Petrov-Galerkin to ensure a local computation of the gradient at the interfaces of the elements. The in-depth study of stability leads to a specific choice of the test functions. With this choice, we show on the one hand that the mixed Petrov-Galerkin obtained is identical to the finite volumes scheme "volumes finis \`a 4 points" ("VF4") of Faille, Gallo\"uet and Herbin and to the condensation of mass approach developed by Baranger, Maitre and Oudin. On the other hand, we show the stability via an inf-sup condition and finally the convergence with the usual methods of mixed finite elements.

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          A mixed finite element method for 2-nd order elliptic problems

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            Finite volume methods

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              Error-bounds for finite element method

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                Author and article information

                Journal
                20 December 2017
                Article
                10.1007/978-3-319-57397-7_27
                1712.08006
                9bf49726-f263-4d7a-a773-cb02128d58cb

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects Springer Proceedings in Mathematics \& Statistics, volume 199, pp.341-349, 2017, \&\#x3008;10.1007/978-3-319-57397-7\_27\&\#x3009
                arXiv admin note: text overlap with arXiv:1710.04395
                math.NA
                ccsd

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