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

• Autorzy: George Avalos , Matthew Dvorak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35M10: Equations of mixed type
• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2008
• Tom: 35
• Numer: 3
• Strony: 259-280

Daty

wydano

2008

Twórcy

autor

George Avalos

• Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, U.S.A.

autor

Matthew Dvorak

• Department of Mathematics, University of Nebraska-Lincoln, Lincoln NE 68588, U.S.A.

Identyfikatory

DOI

10.4064/am35-3-2