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    Discontinuous Galerkin Method for Hyperbolic Conservation Laws

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    Type
    Thesis
    Authors
    Mousikou, Ioanna cc
    Advisors
    Tzavaras, Athanasios cc
    Committee members
    Knio, Omar cc
    Parsani, Matteo cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2016-11-11
    Permanent link to this record
    http://hdl.handle.net/10754/621929
    
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    Abstract
    Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.
    Citation
    Mousikou, I. (2016). Discontinuous Galerkin Method for Hyperbolic Conservation Laws. KAUST Research Repository. https://doi.org/10.25781/KAUST-ZUZKJ
    DOI
    10.25781/KAUST-ZUZKJ
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-ZUZKJ
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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