Space-time adaptive hp-FEM for problems with traveling sharp fronts

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388998%3A_____%2F13%3A00438704" target="_blank" >RIV/61388998:_____/13:00438704 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00607-012-0243-7" target="_blank" >http://dx.doi.org/10.1007/s00607-012-0243-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00607-012-0243-7" target="_blank" >10.1007/s00607-012-0243-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Space-time adaptive hp-FEM for problems with traveling sharp fronts

Popis výsledku v původním jazyce

The hp-FEM is an adaptive version of the Finite Element Method (FEM) that is capable of achieving fast exponential convergence rates by combining optimally spatial refinements (h-adaptivity) with varying element polynomial degrees (p-adaptivity). We present a novel space-time adaptive hp-FEM algorithm that is capable of capturing accurately traveling sharp fronts in nonlinear time-dependent problems. The algorithm tries to assess the true approximation error directly (not via residuals or related techniques), and it does not involve any tuning parameters exposed to the user. The algorithm is compared to non-adaptive FEM as well as to adaptive FEM with low-order elements in the context of a model problem with moving sharp front that consists of two coupled nonlinear parabolic equations. Also the treatment of nonlinear terms is discussed and it is shown that replacing the Newton's method with simpler linearizations can lead to considerable errors.

Název v anglickém jazyce

Space-time adaptive hp-FEM for problems with traveling sharp fronts

Popis výsledku anglicky

The hp-FEM is an adaptive version of the Finite Element Method (FEM) that is capable of achieving fast exponential convergence rates by combining optimally spatial refinements (h-adaptivity) with varying element polynomial degrees (p-adaptivity). We present a novel space-time adaptive hp-FEM algorithm that is capable of capturing accurately traveling sharp fronts in nonlinear time-dependent problems. The algorithm tries to assess the true approximation error directly (not via residuals or related techniques), and it does not involve any tuning parameters exposed to the user. The algorithm is compared to non-adaptive FEM as well as to adaptive FEM with low-order elements in the context of a model problem with moving sharp front that consists of two coupled nonlinear parabolic equations. Also the treatment of nonlinear terms is discussed and it is shown that replacing the Newton's method with simpler linearizations can lead to considerable errors.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computing

ISSN

0010-485X

e-ISSN

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Svazek periodika

95

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

14

Strana od-do

"S709"-"S722"

Kód UT WoS článku

000338630100041

EID výsledku v databázi Scopus

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