A Study of Hyperbolicity of Kinetic Stochastic Galerkin System for the Isentropic Euler Equations with Uncertainty
Shi Jin , Ruiwen Shu
Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (5) : 765 -780.
A Study of Hyperbolicity of Kinetic Stochastic Galerkin System for the Isentropic Euler Equations with Uncertainty
The authors study the fluid dynamic behavior of the stochastic Galerkin (SG for short) approximation to the kinetic Fokker-Planck equation with random uncertainty. While the SG system at the kinetic level is hyperbolic, its fluid dynamic limit, as the Knudsen number goes to zero and the underlying kinetic equation approaches to the uncertain isentropic Euler equations, is not necessarily hyperbolic, as will be shown in the case study fashion for various orders of the SG approximations.
Hyperbolic equations / Uncertainty quantification / Stochastic Galerkin methods
| [1] |
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| [2] |
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| [3] |
|
| [4] |
|
| [5] |
|
| [6] |
|
| [7] |
Gerster, S., Herty, M. M. and Sikstel, A., Hyperbolic stochastic Galerkin formulation for the p-system, to preprint. |
| [8] |
|
| [9] |
|
| [10] |
|
| [11] |
|
| [12] |
Research in Math. Sci., 2017, 4 15 |
| [13] |
|
| [14] |
|
| [15] |
|
| [16] |
|
| [17] |
|
| [18] |
|
| [19] |
|
| [20] |
|
| [21] |
|
| [22] |
|
| [23] |
|
| [24] |
|
| [25] |
|
| [26] |
|
| [27] |
|
| [28] |
|
| [29] |
|
| [30] |
|
| [31] |
|
| [32] |
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