Stability of the ale space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387924" target="_blank" >RIV/00216208:11320/18:10387924 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1051/m2an/2018062" target="_blank" >https://doi.org/10.1051/m2an/2018062</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/m2an/2018062" target="_blank" >10.1051/m2an/2018062</a>

Result language
angličtina
Original language name
Stability of the ale space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains
Original language description
The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of nonstationary nonlinear convection-diffusion initial- boundary value problem in a time-dependent domain. The problem is reformulated using the arbitrary Lagrangian{Eulerian (ALE) method, which replaces the classical partial time derivative by the so-called ALE derivative and an additional convective term. The problem is discretized with the use of the ALE- space time discontinuous Galerkin method (ALE-STDGM). In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diusion terms and interior and boundary penalty. The nonlinear convection terms are discretized with the aid of a numerical flux. The main attention is paid to the proof of the unconditional stability of the method. An important step is the generalization of a discrete characteristic function associated with the approximate solution and the derivation of its properties.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA17-01747S" target="_blank" >GA17-01747S: Theory and numerical analysis of coupled problems in fluid dynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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