A convergent method for linear half-space kinetic equations
Abstract
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations.
Cite
@article{arxiv.1408.6630,
title = {A convergent method for linear half-space kinetic equations},
author = {Qin Li and Jianfeng Lu and Weiran Sun},
journal= {arXiv preprint arXiv:1408.6630},
year = {2016}
}