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.
Accepté le :
DOI : 10.1051/m2an/2016076
Mots-clés : Half-space equations, boundary layer, kinetic-fluid coupling, Galerkin method
@article{M2AN_2017__51_5_1583_0,
author = {Li, Qin and Lu, Jianfeng and Sun, Weiran},
title = {A convergent method for linear half-space kinetic equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1583--1615},
publisher = {EDP-Sciences},
volume = {51},
number = {5},
year = {2017},
doi = {10.1051/m2an/2016076},
mrnumber = {3731542},
zbl = {1380.35006},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016076/}
}
TY - JOUR AU - Li, Qin AU - Lu, Jianfeng AU - Sun, Weiran TI - A convergent method for linear half-space kinetic equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1583 EP - 1615 VL - 51 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016076/ DO - 10.1051/m2an/2016076 LA - en ID - M2AN_2017__51_5_1583_0 ER -
%0 Journal Article %A Li, Qin %A Lu, Jianfeng %A Sun, Weiran %T A convergent method for linear half-space kinetic equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1583-1615 %V 51 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016076/ %R 10.1051/m2an/2016076 %G en %F M2AN_2017__51_5_1583_0
Li, Qin; Lu, Jianfeng; Sun, Weiran. A convergent method for linear half-space kinetic equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1583-1615. doi : 10.1051/m2an/2016076. http://www.numdam.org/articles/10.1051/m2an/2016076/
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