Discontinuous Galerkin Method for Hyperbolic Conservation Laws

Handle URI:
http://hdl.handle.net/10754/621929
Title:
Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Authors:
Mousikou, Ioanna ( 0000-0003-0557-8007 )
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.
Advisors:
Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Committee Member:
Knio, Omar Mohamad; Parsani, Matteo ( 0000-0001-7300-1280 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
11-Nov-2016
Type:
Thesis
Appears in Collections:
Theses

Full metadata record

DC FieldValue Language
dc.contributor.advisorTzavaras, Athanasiosen
dc.contributor.authorMousikou, Ioannaen
dc.date.accessioned2016-12-04T13:48:46Z-
dc.date.available2016-12-04T13:48:46Z-
dc.date.issued2016-11-11-
dc.identifier.urihttp://hdl.handle.net/10754/621929-
dc.description.abstractHyperbolic 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.en
dc.language.isoenen
dc.subjectDiscontinuous Galerkinen
dc.subjectHyperbolic conservation lawsen
dc.subjectsystem of elastodynamicsen
dc.titleDiscontinuous Galerkin Method for Hyperbolic Conservation Lawsen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberKnio, Omar Mohamaden
dc.contributor.committeememberParsani, Matteoen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id143744en
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