Name
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 implemented on parallel computers and applied to more general systems of nonlinear parabolic equations in two- and three-dimensional cases. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/060664872 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
relaxation approximation,diffusive relaxation scheme,Hamilton-Jacobi equation,relaxation term,various numerical result,numerical analysis,Nonlinear Degenerate Diffusion Problems,numerical approximation,nonlinear parabolic equation,High-Order Relaxation Schemes,convergence analysis,proposed numerical scheme | Nonlinear system,Mathematical analysis,Partial differential equation,Degenerate diffusion,Mathematics,Conservation law | Journal |
Volume | Issue | ISSN |
45 | 5 | 0036-1429 |
Citations | PageRank | References |
15 | 1.25 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fausto Cavalli | 1 | 18 | 3.31 |
| Giovanni Naldi | 2 | 45 | 13.96 |
| Gabriella Puppo | 3 | 282 | 51.53 |
| Matteo Semplice | 4 | 64 | 8.16 |