We propose a domain decomposition method for advection-diffusion-reaction equations based on Nitsche’s transmission conditions. The advection-dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries. We prove the convergence of the finite element solutions of the discrete problem to the exact solution and propose a parallelizable iterative method. The convergence of the resulting domain decomposition method is proved, and this result holds true uniformly with respect to the diffusion parameter. The numerical scheme that we propose here can thus be applied straightforwardly to diffusion-dominated, advection-dominated, and hyperbolic problems. Some numerical examples are presented in different flow regimes showing the influence of the stabilization parameter on the performance of the iterative method, and we compare our method with some other domain decomposition techniques for advection-diffusion equations.

A domain decomposition method based on weightd interior penalties for advection-diffusion-reaction problems

ZUNINO, PAOLO
2006

Abstract

We propose a domain decomposition method for advection-diffusion-reaction equations based on Nitsche’s transmission conditions. The advection-dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries. We prove the convergence of the finite element solutions of the discrete problem to the exact solution and propose a parallelizable iterative method. The convergence of the resulting domain decomposition method is proved, and this result holds true uniformly with respect to the diffusion parameter. The numerical scheme that we propose here can thus be applied straightforwardly to diffusion-dominated, advection-dominated, and hyperbolic problems. Some numerical examples are presented in different flow regimes showing the influence of the stabilization parameter on the performance of the iterative method, and we compare our method with some other domain decomposition techniques for advection-diffusion equations.
File in questo prodotto:
File Dimensione Formato  
SNA001612.pdf

Accesso riservato

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 521.24 kB
Formato Adobe PDF
521.24 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/11311/553016
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 75
  • ???jsp.display-item.citation.isi??? ND
social impact