RESIDUAL BASED ERROR ESTIMATES FOR THE SPACE-TIME DISCONTINUOUS GALERKIN METHOD APPLIED TO NONLINEAR HYPERBOLIC EQUATIONS
Result description
We present an adaptive numerical method for solving nonlinear hyperbolic equations. The method uses the space-time discontinuous Galerkin discretization, exploiting its high polynomial approximation degrees with respect to both space and time coordinates. We derive an residual based a posteriori error estimator and propose an efficient strategy how to identify the parts of the computational error caused by the space and time discretization, respectively, as well as the errors arising from the linearization of the resultant algebraic system of equations. Further, an algorithm keeping all these three components of the computational error balanced is presented. The computational performance of the proposed method is demonstrated by numerical experiments.
Keywords
residual-based a posteriori error estimatesspace-time discontinuous Galerkin methodnonlinear hyperbolic equation
The result's identifiers
Result code in IS VaVaI
Result on the web
http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/issue/view/19
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
RESIDUAL BASED ERROR ESTIMATES FOR THE SPACE-TIME DISCONTINUOUS GALERKIN METHOD APPLIED TO NONLINEAR HYPERBOLIC EQUATIONS
Original language description
We present an adaptive numerical method for solving nonlinear hyperbolic equations. The method uses the space-time discontinuous Galerkin discretization, exploiting its high polynomial approximation degrees with respect to both space and time coordinates. We derive an residual based a posteriori error estimator and propose an efficient strategy how to identify the parts of the computational error caused by the space and time discretization, respectively, as well as the errors arising from the linearization of the resultant algebraic system of equations. Further, an algorithm keeping all these three components of the computational error balanced is presented. The computational performance of the proposed method is demonstrated by numerical experiments.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
PROCEEDINGS OF THE CONFERENCE ALGORITMY 2016
ISBN
978-80-227-4544-4
ISSN
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e-ISSN
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Number of pages
12
Pages from-to
113-124
Publisher name
SLOVAK UNIV TECH BRATISLAVA
Place of publication
BRATISLAVA
Event location
Vysoke Tatry
Event date
Mar 14, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000391175600012
Basic information
Result type
D - Article in proceedings
CEP
BA - General mathematics
Year of implementation
2016