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

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Original languageEnglish
Article number40
Journal / PublicationJournal of Scientific Computing
Issue number2
Online published10 Aug 2020
Publication statusPublished - Aug 2020


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.

Research Area(s)

  • Interface problems, Local optimal error estimate, Low regularity, Mixed finite element method, Robust a priori error estimate