Linearly Implicit Approximations of Diffusive Relaxation Systems

Fausto Cavalli

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

1 Citazioni (Scopus)

Abstract

Diffusive relaxation systems provide a general framework to approximate nonlinear diffusion problems, also in the degenerate case (Aregba-Driollet et al. in Math. Comput. 73(245):63-94, 2004; Boscarino et al. in Implicit-explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit, 2011; Cavalli et al. in SIAM J. Sci. Comput. 34:A137-A160, 2012; SIAM J. Numer. Anal. 45(5):2098-2119, 2007; Naldi and Pareschi in SIAM J. Numer. Anal. 37:1246-1270, 2000; Naldi et al. in Surveys Math. Indust. 10(4):315-343, 2002). Their discretization is usually obtained by explicit schemes in time coupled with a suitable method in space, which inherits the standard stability parabolic constraint. In this paper we combine the effectiveness of the relaxation systems with the computational efficiency and robustness of the implicit approximations, avoiding the need to resolve nonlinear problems and avoiding stability constraints on time step. In particular we consider an implicit scheme for the whole relaxation system except for the nonlinear source term, which is treated though a suitable linearization technique. We give some theoretical stability results in a particular case of linearization and we provide insight on the general case. Several numerical simulations confirm the theoretical results and give evidence of the stability and convergence also in the case of nonlinear degenerate diffusion.
Lingua originaleEnglish
pagine (da-a)79-103
Numero di pagine25
RivistaActa Applicandae Mathematicae
Volume125
DOI
Stato di pubblicazionePubblicato - 2012

Keywords

  • Finite difference
  • Linear implicit methods
  • Nonlinear diffusion
  • Relaxation systems

Fingerprint

Entra nei temi di ricerca di 'Linearly Implicit Approximations of Diffusive Relaxation Systems'. Insieme formano una fingerprint unica.

Cita questo