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Robust and Local Optimal A Priori Error Estimates for Interface Problems with Low Regularity: Mixed Finite Element Approximations

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Abstract

For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart–Thomas and Brezzi–Douglas–Marini mixed finite element approximations. These estimates are robust with respect to the diffusion coefficient and optimal with respect to the local regularity of the solution. Several versions of the robust best approximations of the flux and the potential approximations are obtained. These robust and local optimal a priori estimates provide guidance for constructing robust a posteriori error estimates and adaptive methods for the mixed approximations.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong SAR, China

    Shun Zhang

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  1. Shun Zhang
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Correspondence to Shun Zhang.

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This work was supported in part by Hong Kong Research Grants Council under the GRF Grant Project No. CityU 11305319.

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Zhang, S. Robust and Local Optimal A Priori Error Estimates for Interface Problems with Low Regularity: Mixed Finite Element Approximations. J Sci Comput 84, 40 (2020). https://doi.org/10.1007/s10915-020-01284-z

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