HOMOGENIZATION OF THE TRANSPORT EQUATION DESCRIBING CONVECTION-DIFFUSION PROCESSES IN A MATERIAL WITH FINE PERIODIC STRUCTURE
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F23%3A00369287" target="_blank" >RIV/68407700:21110/23:00369287 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.21136/panm.2022.22" target="_blank" >https://doi.org/10.21136/panm.2022.22</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/panm.2022.22" target="_blank" >10.21136/panm.2022.22</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
HOMOGENIZATION OF THE TRANSPORT EQUATION DESCRIBING CONVECTION-DIFFUSION PROCESSES IN A MATERIAL WITH FINE PERIODIC STRUCTURE
Popis výsledku v původním jazyce
In the present contribution we discuss mathematical homoge- nization and numerical solution of the elliptic problem describing convection- diusion processes in a material with ne periodic structure. Transport pro- cesses such as heat conduction or transport of contaminants through porous media are typically associated with convection-diusion equations. It is well known that the application of the classical Galerkin nite element method is in- appropriate in this case since the discrete solution is usually globally aected by spurious oscillations. Therefore, great care should be taken in develop- ing stable numerical formulations. We describe a variational principle for the convection-diusion problem with rapidly oscillating coecients and formulate the corresponding homogenization results. Further, based on the variational principle, we derive a stable numerical scheme for the corresponding homog- enized problem. A numerical example will be solved to illustrate the overall performance of the proposed method.
Název v anglickém jazyce
HOMOGENIZATION OF THE TRANSPORT EQUATION DESCRIBING CONVECTION-DIFFUSION PROCESSES IN A MATERIAL WITH FINE PERIODIC STRUCTURE
Popis výsledku anglicky
In the present contribution we discuss mathematical homoge- nization and numerical solution of the elliptic problem describing convection- diusion processes in a material with ne periodic structure. Transport pro- cesses such as heat conduction or transport of contaminants through porous media are typically associated with convection-diusion equations. It is well known that the application of the classical Galerkin nite element method is in- appropriate in this case since the discrete solution is usually globally aected by spurious oscillations. Therefore, great care should be taken in develop- ing stable numerical formulations. We describe a variational principle for the convection-diusion problem with rapidly oscillating coecients and formulate the corresponding homogenization results. Further, based on the variational principle, we derive a stable numerical scheme for the corresponding homog- enized problem. A numerical example will be solved to illustrate the overall performance of the proposed method.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
S - Specificky vyzkum na vysokych skolach
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
PANM 21: Proceedings of 21st conference, Janov nad Nisou, 2022
ISBN
978-80-85823-73-8
ISSN
—
e-ISSN
—
Počet stran výsledku
10
Strana od-do
239-248
Název nakladatele
Matematický ústav AV ČR, v. v. i.
Místo vydání
Praha
Místo konání akce
Jablonec nad Nisou
Datum konání akce
19. 6. 2022
Typ akce podle státní příslušnosti
WRD - Celosvětová akce
Kód UT WoS článku
—