Numerical approximation of planar oblique derivative problems in nondivergence form

D. Gallistl (Corresponding Author)

    Research output: Contribution to journalArticleAcademicpeer-review

    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

    Fingerprint

    Oblique
    Numerical Approximation
    Derivatives
    Derivative
    Numerical methods
    Affine Function
    Adaptive Mesh
    Mixed Formulation
    A Posteriori Error Estimates
    Boundary conditions
    Numerical Computation
    Numerical Scheme
    Numerical Methods
    Finite Element
    Gradient
    Approximation
    Form

    Keywords

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

    Cite this

    @article{eb50d85aaf724dfe8d9fe2f399b47b73,
    title = "Numerical approximation of planar oblique derivative problems in nondivergence form",
    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.",
    keywords = "Cordes coefficents, Oblique derivative problem, a posteriori error analysis, a priori error analysis, nondivergence form",
    author = "D. Gallistl",
    year = "2019",
    month = "5",
    doi = "10.1090/mcom/3371",
    language = "English",
    volume = "88",
    pages = "1091--1119",
    journal = "Mathematics of computation",
    issn = "0025-5718",
    publisher = "American Mathematical Society",
    number = "317",

    }

    Numerical approximation of planar oblique derivative problems in nondivergence form. / Gallistl, D. (Corresponding Author).

    In: Mathematics of computation, Vol. 88, No. 317, 05.2019, p. 1091-1119.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Numerical approximation of planar oblique derivative problems in nondivergence form

    AU - Gallistl, D.

    PY - 2019/5

    Y1 - 2019/5

    N2 - 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.

    AB - 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.

    KW - Cordes coefficents

    KW - Oblique derivative problem

    KW - a posteriori error analysis

    KW - a priori error analysis

    KW - nondivergence form

    UR - http://www.scopus.com/inward/record.url?scp=85064505255&partnerID=8YFLogxK

    U2 - 10.1090/mcom/3371

    DO - 10.1090/mcom/3371

    M3 - Article

    VL - 88

    SP - 1091

    EP - 1119

    JO - Mathematics of computation

    JF - Mathematics of computation

    SN - 0025-5718

    IS - 317

    ER -