Geodesic
A convergent method for linear half-space kinetic equations
Li, Qin1 ; Lu, Jianfeng2   ; Sun, Weiran3
1 Computing and Mathematical Sciences, California Institute of Technology, 1200 E California Blvd. MC 305-16, Pasadena, CA 91125 USA.
2 Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Box 90320, Durham, NC 27708 USA.
3 Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC V5A 1S6, Canada.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1583-1615

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016076
Classification : 35F15, 35Q79
Keywords: Half-space equations, boundary layer, kinetic-fluid coupling, Galerkin method

Li, Qin 1 ; Lu, Jianfeng 2 ; Sun, Weiran 3

1 Computing and Mathematical Sciences, California Institute of Technology, 1200 E California Blvd. MC 305-16, Pasadena, CA 91125 USA.
2 Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Box 90320, Durham, NC 27708 USA.
3 Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC V5A 1S6, Canada. 
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     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},
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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

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