Stability estimates for h-p spectral element methods for general elliptic problems on curvilinear domains

Pravir Dutt, Satyendra Tomar

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    14 Citations (Scopus)

    Abstract

    In this paper we show that the h-p spectral element method developed in 3,8,9 applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska–Brezzi inf-sup conditions are satisfied. We establish basic stability estimates for a non-conforming h-p spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-conforming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are continuous only at the vertices of the elements. We obtain a stability estimate when the spectral element functions vanish at the vertices of the elements, which is needed for parallelizing the numerical scheme. Finally, we indicate how the mesh refinement strategy and choice of polynomial degree depends on the regularity of the coefficients of the differential operator, smoothness of the sides of the polygon and the regularity of the data to obtain the maximum accuracy achievable.
    Original languageEnglish
    Pages (from-to)395-429
    Number of pages35
    JournalProceedings of the Indian academy of sciences - mathematical sciences
    Volume113
    Issue number4
    DOIs
    Publication statusPublished - Nov 2003

    Keywords

    • IR-70531
    • curvilinear polygons
    • geometrical mesh
    • METIS-213783
    • mixed Neumann Dirichlet boundary conditions
    • fractional Sobolev norms
    • infsup conditions
    • stability estimates
    • Corner singularities - geometrical mesh - mixed Neumann and Dirichlet boundary conditions - curvilinear polygons - inf-sup conditions - stability estimates - fractional Sobolev norms
    • Corner singularities
    • EWI-16210

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