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    A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity

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    Type
    Article
    Authors
    Demkowicz, Leszek
    Gopalakrishnan, Jay
    Niemi, Antti H.
    Date
    2012-04
    Permanent link to this record
    http://hdl.handle.net/10754/597230
    
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    Abstract
    We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: ε=10 -11 for 1D and ε=10 -7 for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only. © 2011 IMACS. Published by Elsevier B.V. All rights reserved.
    Citation
    Demkowicz L, Gopalakrishnan J, Niemi AH (2012) A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity. Applied Numerical Mathematics 62: 396–427. Available: http://dx.doi.org/10.1016/j.apnum.2011.09.002.
    Sponsors
    Demkowicz was supported in part by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615], and by a research contract with Boeing. Gopalakrishnan was supported in part by the National Science Foundation under grant DMS-0713833. Niemi was supported in part by KAUST. We thank Bob Moser and David Young for encouragement and stimulating discussions on the project.
    Publisher
    Elsevier BV
    Journal
    Applied Numerical Mathematics
    DOI
    10.1016/j.apnum.2011.09.002
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.apnum.2011.09.002
    Scopus Count
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