Numerical approximation of planar oblique derivative problems in nondivergence form

D. Gallistl (Corresponding Author)

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    2 Citations (Scopus)

    Abstract

    A numerical method for approximating a uniformly elliptic oblique derivative problem in two-dimensional simply-connected domains is proposed. The numerical scheme employs a mixed formulation with piecewise affine functions on curved finite element domains. The direct approximation of the gradient of the solution turns the oblique derivative boundary condition into an oblique direction condition. A priori and a posteriori error estimates as well as numerical computations on uniform and adaptive meshes are provided.
    Original languageEnglish
    Pages (from-to)1091-1119
    Number of pages29
    JournalMathematics of computation
    Volume88
    Issue number317
    DOIs
    Publication statusPublished - May 2019

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    Keywords

    • Cordes coefficents
    • Oblique derivative problem
    • a posteriori error analysis
    • a priori error analysis
    • nondivergence form

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