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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

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

Name of the periodical

Computing

ISSN

0010-485X

e-ISSN

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Volume of the periodical

95

Issue of the periodical within the volume

1

Country of publishing house

AT - AUSTRIA

Number of pages

14

Pages from-to

"S709"-"S722"

UT code for WoS article

000338630100041

EID of the result in the Scopus database

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