Name
Abstract | ||
|---|---|---|
We propose and analyze several finite difference schemes for the Hunter-Saxton equation [GRAPHICS] This equation has been suggested as a simple model for nematic liquid crystals. We prove that the numerical approximations converge to the unique dissipative solution of (HS), as identified by Zhang and Zheng. A main aspect of the analysis, in addition to the derivation of several a priori estimates that yield some basic convergence results, is to prove strong convergence of the discrete spatial derivative of the numerical approximations of u, which is achieved by analyzing various renormalizations (in the sense of DiPerna and Lions) of the numerical schemes. Finally, we demonstrate through several numerical examples the proposed schemes as well as some other schemes for which we have no rigorous convergence results. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1090/S0025-5718-07-01919-9 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Hunter-Saxton equation,finite difference schemes,weak solutions,convergence,liquid crystals | Renormalization,Convergence (routing),Mathematical analysis,Finite difference,A priori and a posteriori,Dissipative system,Hunter–Saxton equation,Finite difference method,Numerical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
76 | 258 | 0025-5718 |
Citations | PageRank | References |
1 | 0.42 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Helge Holden | 1 | 63 | 11.29 |
| Kenneth H. Karlsen | 2 | 119 | 23.76 |
| Nils Henrik Risebro | 3 | 79 | 38.95 |