A FEM approximation of a two-phase obstacle problem and its a posteriori error estimate

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00470507" target="_blank" >RIV/67985556:_____/17:00470507 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/60076658:12310/17:43895473

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.camwa.2016.11.037" target="_blank" >http://dx.doi.org/10.1016/j.camwa.2016.11.037</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2016.11.037" target="_blank" >10.1016/j.camwa.2016.11.037</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A FEM approximation of a two-phase obstacle problem and its a posteriori error estimate

Popis výsledku v původním jazyce

This paper is concerned with the two-phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A solution algorithm is proposed for the construction of the finite element approximation to the two-phase obstacle problem. The algorithm is not based on the primal (convex and nondifferentiable) energy minimization problem but on a dual maximization problem formulated for Lagrange multipliers. The dual problem is equivalent to a quadratic programming problem with box constraints. The quality of approximations is measured by a functional a posteriori error estimate which provides a guaranteed upper bound of the difference of approximated and exact energies of the primal minimization problem. The majorant functional in thenupper bound contains auxiliary variables and it is optimized with respect to them to provide a sharp upper bound.

Název v anglickém jazyce

A FEM approximation of a two-phase obstacle problem and its a posteriori error estimate

Popis výsledku anglicky

This paper is concerned with the two-phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A solution algorithm is proposed for the construction of the finite element approximation to the two-phase obstacle problem. The algorithm is not based on the primal (convex and nondifferentiable) energy minimization problem but on a dual maximization problem formulated for Lagrange multipliers. The dual problem is equivalent to a quadratic programming problem with box constraints. The quality of approximations is measured by a functional a posteriori error estimate which provides a guaranteed upper bound of the difference of approximated and exact energies of the primal minimization problem. The majorant functional in thenupper bound contains auxiliary variables and it is optimized with respect to them to provide a sharp upper bound.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Computers & Mathematics With Applications

ISSN

0898-1221

e-ISSN

—

Svazek periodika

73

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

14

Strana od-do

419-432

Kód UT WoS článku

000394199100005

EID výsledku v databázi Scopus

2-s2.0-85008199888