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    FEM Convergence Studies for 2-D and 3-D Elliptic PDEs with Smooth and Non-Smooth Source Terms in COMSOL 5.1

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    COMSOL51_HPCF2015.pdf (608.0Kb)
    Links to Files
    https://userpages.umbc.edu/~gobbert/papers/COMSOL51_HPCF2015.pdf
    Permanent Link
    http://hdl.handle.net/11603/11427
    Collections
    • UMBC Faculty Collection
    • UMBC Mathematics and Statistics Department
    • UMBC Mechanical Engineering Department
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    Author/Creator
    Kalayeh, Kourosh M.
    Graf, Jonathan S.
    Gobbert, Matthias K.
    Date
    2015
    Type of Work
    10 pages
    Text
    techical report
    Rights
    This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
    Subjects
    Poisson equation
    point source
    Dirac delta distribution
    convergence study
    mesh refinement
    UMBC High Performance Computing Facility (HPCF)
    Abstract
    Numerical theory provides the basis for quanti cation on the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in COMSOL 5.1 to perform computational studies for an elliptic test problem in two and three space dimensions that demonstrate this theory by computing the convergence order of the FEM error. For a PDE with smooth right-hand side, linear Lagrange nite elements exhibit second order convergence for all space dimensions. We also show how to perform these techniques for a problem involving a point source modeled by a Dirac delta distribution as forcing term. This demonstrates that PDE problems with a non-smooth source term necessarily have degraded convergence order and thus can be most e ciently solved by low-order FEM such as linear Lagrange elements. Detailed instructions for obtaining the results are included in an appendix.


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3544


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.