We propose a finite element scheme for the approximation of multidomain heterogeneous problems arising in the general framework of linear incompressible flows (e.g. Stokes' and Darcy's equations). We exploit stabilized mixed finite elements together with Nitsche type matching conditions that automatically adapt to the coupling of different subproblem combinations. Optimal error estimates are derived for the coupled problem. Then, we propose and analyze an iterative splitting strategy for the approximation of the multidomain solution by means of a sequence of independent and local subproblems. Thanks to the introduction of a suitable relaxation strategy,the iterative method turns out to be convergent for any possible coupling between subproblems.

A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows

D'ANGELO, CARLO;ZUNINO, PAOLO
2009

Abstract

We propose a finite element scheme for the approximation of multidomain heterogeneous problems arising in the general framework of linear incompressible flows (e.g. Stokes' and Darcy's equations). We exploit stabilized mixed finite elements together with Nitsche type matching conditions that automatically adapt to the coupling of different subproblem combinations. Optimal error estimates are derived for the coupled problem. Then, we propose and analyze an iterative splitting strategy for the approximation of the multidomain solution by means of a sequence of independent and local subproblems. Thanks to the introduction of a suitable relaxation strategy,the iterative method turns out to be convergent for any possible coupling between subproblems.
generalized Stokes problem; Darcy problem; discontinuous coefficients; finite element approximation; interior penalty; iterative splitting methods
File in questo prodotto:
File Dimensione Formato  
SINUM-072631RR.pdf

Accesso riservato

: Pre-Print (o Pre-Refereeing)
Dimensione 392.8 kB
Formato Adobe PDF
392.8 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/560591
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 13
social impact