A new maximality argument for a coupled fluid-structure interaction, with implications for a divergence-free finite element method

George Avalos, and Matthew Dvorak. "A new maximality argument for a coupled fluid-structure interaction, with implications for a divergence-free finite element method." Applicationes Mathematicae 35.3 (2008): 259-280. <http://eudml.org/doc/280044>.

@article{GeorgeAvalos2008,
abstract = {We consider a coupled PDE model of various fluid-structure interactions seen in nature. It has recently been shown by the authors [Contemp. Math. 440, 2007] that this model admits of an explicit semigroup generator representation 𝓐:D(𝓐)⊂ H → H, where H is the associated space of fluid-structure initial data. However, the argument for the maximality criterion was indirect, and did not provide for an explicit solution Φ ∈ D(𝓐) of the equation (λI-𝓐)Φ =F for given F ∈ H and λ > 0. The present work reconsiders the proof of maximality for the fluid-structure generator 𝓐, and gives an explicit method for solving the said fluid-structure equation. This involves a nonstandard usage of the Babuška-Brezzi Theorem. Subsequently, a finite element method for approximating solutions of the fluid-structure dynamics is developed, based upon our explicit proof of maximality.},
author = {George Avalos, Matthew Dvorak},
journal = {Applicationes Mathematicae},
keywords = {elimination of pressure; fluid-structure generator; maximal dissipative operator; Ritz-Galerkin method; explicit method; Babuška-Brezzi theorem},
language = {eng},
number = {3},
pages = {259-280},
title = {A new maximality argument for a coupled fluid-structure interaction, with implications for a divergence-free finite element method},
url = {http://eudml.org/doc/280044},
volume = {35},
year = {2008},
}

TY - JOUR
AU - George Avalos
AU - Matthew Dvorak
TI - A new maximality argument for a coupled fluid-structure interaction, with implications for a divergence-free finite element method
JO - Applicationes Mathematicae
PY - 2008
VL - 35
IS - 3
SP - 259
EP - 280
AB - We consider a coupled PDE model of various fluid-structure interactions seen in nature. It has recently been shown by the authors [Contemp. Math. 440, 2007] that this model admits of an explicit semigroup generator representation 𝓐:D(𝓐)⊂ H → H, where H is the associated space of fluid-structure initial data. However, the argument for the maximality criterion was indirect, and did not provide for an explicit solution Φ ∈ D(𝓐) of the equation (λI-𝓐)Φ =F for given F ∈ H and λ > 0. The present work reconsiders the proof of maximality for the fluid-structure generator 𝓐, and gives an explicit method for solving the said fluid-structure equation. This involves a nonstandard usage of the Babuška-Brezzi Theorem. Subsequently, a finite element method for approximating solutions of the fluid-structure dynamics is developed, based upon our explicit proof of maximality.
LA - eng
KW - elimination of pressure; fluid-structure generator; maximal dissipative operator; Ritz-Galerkin method; explicit method; Babuška-Brezzi theorem
UR - http://eudml.org/doc/280044
ER -