Name
Abstract | ||
|---|---|---|
Three fully discrete finite element methods are developed for approximating wave maps into the sphere based on two different approaches. The first method is an explicit scheme and the numerical solution satisfies the sphere-constraint exactly at every node. The second and third methods are implicit schemes which are based on a penalization approach, their numerical solutions satisfy the sphere-constraint approximately, and the quality of approximations is controlled by a small penalization parameter. Discrete energy conservation laws which mimic the underlying differential conservation law are established, and convergence of all proposed methods is proved. Computational experiments are also provided to validate the proposed methods and to present numerical evidence for possible finite-time blow-ups of the wave maps. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/060659971 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
approximating wave map,underlying differential conservation law,numerical evidence,finite element approximations,discrete energy conservation law,wave maps,discrete finite element method,penalization approach,wave map,numerical solution,small penalization parameter,energy conservation,satisfiability,conservation law,computer experiment,finite element method | Convergence (routing),Energy conservation,Mathematical optimization,Mathematical analysis,Finite element method,Finite element approximations,SPHERES,Numerical analysis,Mathematics,Conservation law | Journal |
Volume | Issue | ISSN |
46 | 1 | 0036-1429 |
Citations | PageRank | References |
5 | 0.65 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sören Bartels | 1 | 355 | 56.90 |
| Xiaobing Feng | 2 | 906 | 112.55 |
| Andreas Prohl | 3 | 302 | 67.29 |