Name
Title | ||
|---|---|---|
Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations |
Abstract | ||
|---|---|---|
The paper is concerned with the unconditional stability and convergence of characteristics type methods for the time-dependent Navier---Stokes equations. We present optimal error estimates in $$L^2$$L2 and $$H^1$$H1 norms for a typical modified characteristics finite element method unconditionally, while all previous works require certain time-step restrictions. The analysis is based on an iterated characteristic time-discrete system, with which the error function is split into a temporal error and a spatial error. With a rigorous analysis to the characteristic time-discrete system, we prove that the difference between the numerical solution and the solution of the time-discrete system is $$\\tau $$¿-independent, where $$\\tau $$¿ denotes the time stepsize. Thus numerical solution in $$W^{1,\\infty }$$W1,¿ is bounded and optimal error estimates can be obtained in a traditional way. Numerical results confirm our analysis and show clearly the unconditional stability and convergence of the modified characteristics finite element method for the time-dependent Navier---Stokes equations. The approach used in this paper can be easily extended to many other characteristics-based methods. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s00211-015-0767-9 | Numerische Mathematik |
Keywords | DocType | Volume |
76M10, 65N12, 65N30, 35K61 | Journal | 134 |
Issue | ISSN | Citations |
1 | 0945-3245 | 10 |
PageRank | References | Authors |
0.61 | 15 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhiyong Si | 1 | 21 | 5.60 |
| Jilu Wang | 2 | 24 | 2.43 |
| Weiwei Sun | 3 | 154 | 15.12 |