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- Title
UNIFORM SPECTRAL CONVERGENCE OF THE STOCHASTIC GALERKIN METHOD FOR THE LINEAR SEMICONDUCTOR BOLTZMANN EQUATION WITH RANDOM INPUTS AND DIFFUSIVE SCALING.
- Authors
Liu, Liu
- Abstract
In this paper, we study the generalized polynomial chaos (gPC) based stochastic Galerkin method for the linear semiconductor Boltzmann equation under diffusive scaling and with random inputs from an anisotropic collision kernel and the random initial condition. While the numerical scheme and the proof of uniform-in-Knudsen-number regularity of the distribution function in the random space has been introduced in [15], the main goal of this paper is to first obtain a sharper estimate on the regularity of the solution{an exponential decay towards its local equilibrium, which then lead to the uniform spectral convergence of the stochastic Galerkin method for the problem under study.
- Subjects
STOCHASTIC convergence; GALERKIN methods; LINEAR equations; SEMICONDUCTORS; BOLTZMANN'S equation; POLYNOMIAL chaos
- Publication
Kinetic & Related Models, 2018, Vol 11, Issue 5, p1139
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2018044