Show simple item record

dc.contributor.advisorTzavaras, Athanasios
dc.contributor.authorMousikou, Ioanna
dc.date.accessioned2016-12-04T13:48:46Z
dc.date.available2016-12-04T13:48:46Z
dc.date.issued2016-11-11
dc.identifier.doi10.25781/KAUST-ZUZKJ
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.
dc.language.isoen
dc.subjectDiscontinuous Galerkin
dc.subjectHyperbolic conservation laws
dc.subjectsystem of elastodynamics
dc.titleDiscontinuous Galerkin Method for Hyperbolic Conservation Laws
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberKnio, Omar Mohamad
dc.contributor.committeememberParsani, Matteo
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science
refterms.dateFOA2018-06-13T15:31:52Z


Files in this item

Thumbnail
Name:
Thesis.pdf
Size:
850.7Kb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record