Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton–Jacobi equations, convection-diffusion problems, and gas dynamics problems. The present paper focuses on diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These schemes are based on a suitable semilinear hyperbolic system with relaxation terms. High-order methods are obtained by coupling ENO and weighted essentially nonoscillatory (WENO) schemes for space discretization with implicit-explicit (IMEX) schemes for time integration. Error estimates and a convergence analysis are developed for semidiscrete schemes with a numerical analysis for fully discrete relaxed schemes. Various numerical results in one and two dimensions illustrate the high accuracy and good properties of the proposed numerical schemes, also in the degenerate case. These schemes can be easily imple- mented on parallel computers and applied to more general systems of nonlinear parabolic equations in two- and three-dimensional cases.

High order relaxation schemes for non linear degenerate diffusion problems / F., Cavalli; G., Naldi; Puppo, G.; M., Semplice. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 45, N. 5:(2007), pp. 2098-2119.

High order relaxation schemes for non linear degenerate diffusion problems

PUPPO G.;
2007

Abstract

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton–Jacobi equations, convection-diffusion problems, and gas dynamics problems. The present paper focuses on diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These schemes are based on a suitable semilinear hyperbolic system with relaxation terms. High-order methods are obtained by coupling ENO and weighted essentially nonoscillatory (WENO) schemes for space discretization with implicit-explicit (IMEX) schemes for time integration. Error estimates and a convergence analysis are developed for semidiscrete schemes with a numerical analysis for fully discrete relaxed schemes. Various numerical results in one and two dimensions illustrate the high accuracy and good properties of the proposed numerical schemes, also in the degenerate case. These schemes can be easily imple- mented on parallel computers and applied to more general systems of nonlinear parabolic equations in two- and three-dimensional cases.
2007
parabolic problems, relaxation schemes, high-order accuracy, porous media equation, WENO reconstruction
01 Pubblicazione su rivista::01a Articolo in rivista
High order relaxation schemes for non linear degenerate diffusion problems / F., Cavalli; G., Naldi; Puppo, G.; M., Semplice. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 45, N. 5:(2007), pp. 2098-2119.
File allegati a questo prodotto
File Dimensione Formato  
Cavalli_High-order-relaxation_2007.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 478.4 kB
Formato Adobe PDF
478.4 kB Adobe PDF   Contatta l'autore

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: https://hdl.handle.net/11573/1280488
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 49
  • ???jsp.display-item.citation.isi??? ND
social impact