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    High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations

    Access Status
    Fulltext not available
    Authors
    Zou, Q.
    Guo, L.
    Deng, Quanling
    Date
    2017
    Type
    Journal Article
    
    Metadata
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    Citation
    Zou, Q. and Guo, L. and Deng, Q. 2017. High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations. SIAM Journal of Numerical Analysis. 55 (6): pp. 2666-2686.
    Source Title
    SIAM Journal of Numerical Analysis
    DOI
    10.1137/16M1066567
    ISSN
    0036-1429
    School
    School of Earth and Planetary Sciences (EPS)
    URI
    http://hdl.handle.net/20.500.11937/65703
    Collection
    • Curtin Research Publications
    Abstract

    © 2017 Society for Industrial and Applied Mathematics. We derive a high order globally continuous and locally conservative flux field and a high order finite-volume-like solution from the continuous Galerkin (CG) finite element solution. The main idea is to postprocess the CG solution by solving a small linear algebraic system on each element of the underlying mesh. Both the postprocessed flux field and the finite-volume-like solution satisfy the conservation law on each control volume of the dual mesh. Moreover, both the postprocessed flux field and the gradient of finite-volume-like solution converge to the exact flux with optimal convergence rates. Our theoretical findings are validated by our numerical experiments.

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