Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses onto diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These schemes are based on suitable semilinear hyperbolic system with relaxation terms. High order methods are obtained by coupling ENO and WENO schemes for space discretization with IMEX schemes for time integration. Error estimates and convergence analysis are developed for semidiscrete schemes with numerical analysis for fully discrete relaxed schemes. Various numerical results in one and two dimension illustrate the high accuracy and good properties of the proposed numerical schemes. These schemes can be easily implemented for parallel computer and applied to more general system of nonlinear parabolic equations in two- and three-dimensional cases.
|Titolo:||High order relaxation schemes for non linear diffusion problems|
|Data di pubblicazione:||2006|
|Parole Chiave:||Relaxation approximation, high order methods, IMEX schemes, ENO-WENO schemes|
|Settore Scientifico Disciplinare:||Settore MAT/08 - Analisi Numerica|
|Enti collegati:||Dipartimento di Matematica, Politecnico di Torino|
|Citazione:||High order relaxation schemes for non linear diffusion problems / Fausto Cavalli, Giovanni Naldi, Gabriella Puppo, Matteo Semplice. - [s.l] : null, 2006.|
|Appare nelle tipologie:||08 - Relazione interna o rapporto di ricerca|