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Mixed finite element methods for the Oseen problem

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Abstract

The aim of this paper is to develop and analyze mixed finite element methods for the Oseen problem using the tensor gradient of velocity as a new unknown. We prove that the new variational formulation and the corresponding Galerkin scheme are well-posed. We also provide optimal order error estimates for the velocity, the pressure, and the gradient of velocity when each row of the velocity gradient is approximated by Raviart–Thomas elements and the velocity and the pressure are approximated by discontinuous piecewise polynomials.

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  1. Département de Mathématiques et de Statistique, Université de Moncton, Moncton, NB, E1A 3E9, Canada

    Mohamed Farhloul

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  1. Mohamed Farhloul
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Correspondence to Mohamed Farhloul.

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Farhloul, M. Mixed finite element methods for the Oseen problem. Numer Algor 84, 1431–1442 (2020). https://doi.org/10.1007/s11075-020-00879-9

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  • DOI: https://doi.org/10.1007/s11075-020-00879-9

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