Analysis and application of the discontinuous Galerkin method to the RLW equation

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dc.contributor.authorHozman, Jiří
dc.contributor.authorLamač, Jan
dc.date.accessioned2016-05-24
dc.date.available2016-05-24
dc.date.issued2013
dc.description.abstractIn this work, our main purpose is to develop of a sufficiently robust, accurate and efficient numerical scheme for the solution of the regularized long wave (RLW) equation, an important partial differential equation with quadratic nonlinearity, describing a large number of physical phenomena. The crucial idea is based on the discretization of the RLW equation with the aid of a combination of the discontinuous Galerkin method for the space semi-discretization and the backward difference formula for the time discretization. Furthermore, a suitable linearization preserves a linear algebraic problem at each time level. We present error analysis of the proposed scheme for the case of nonsymmetric discretization of the dispersive term. The appended numerical experiments confirm theoretical results and investigate the conservative properties of the RLW equation related to mass, momentum and energy. Both procedures illustrate the potency of the scheme consequently.en
dc.description.sponsorshipESF [CZ.1.07/2.3.00/09.0155]; SGS Project 'Modern numerical methods'; TU Liberec
dc.formattext
dc.identifier.doi10.1186/1687-2770-2013-116
dc.identifier.issn1687-2770
dc.identifier.scopus2-s2.0-84888018196
dc.identifier.urihttps://dspace.tul.cz/handle/15240/16347
dc.language.isoen
dc.publisherSpringer International Publishing Ag
dc.publisherTechnical university of Liberec, Czech Republicen
dc.publisherTechnická Univerzita v Libercics
dc.relation.ispartofBoundary Value Problemsen
dc.sourcej-scopus
dc.sourcej-wok
dc.subjectdiscontinuous Galerkin methoden
dc.subjectregularized long wave equationen
dc.subjectbackward Euler methoden
dc.subjectlinearizationen
dc.subjectsemi-implicit schemeen
dc.subjectpriori error estimatesen
dc.subjectsolitary and periodic wave solutionsen
dc.subjectexperimental order of convergenceen
dc.titleAnalysis and application of the discontinuous Galerkin method to the RLW equationen
dc.typeArticle
local.accessοpen
local.citation.epage20
local.citation.spage1
local.departmentDepartment of Mathematics and Didactics of Mathematics
local.facultyFaculty of Sciences, Humanities and Education
local.fulltextyes
local.identifier.stagRIV/46747885:24510/13:#0001000
local.identifier.wok320662500001
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