High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems

Fausto Cavalli, Giovanni Naldi, Gabriella Puppo, Matteo Semplice

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33 Citazioni (Scopus)


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 bycoupling 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 implemented on parallel computers and applied to more general systems of nonlinear parabolic equations in two- and three-dimensional cases.
Lingua originaleEnglish
pagine (da-a)2098-2119
Numero di pagine22
RivistaSIAM Journal on Numerical Analysis
Stato di pubblicazionePubblicato - 2007


  • High-order accuracy
  • Parabolic problems
  • Porous media equation
  • Relaxation schemes
  • WENO reconstruction

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