A convergent method for linear half-space kinetic equations

Qin Li; Jianfeng Lu; Weiran Sun

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arXiv · 1408.6630

A convergent method for linear half-space kinetic equations

Qin Li·Jianfeng Lu·Weiran Sun

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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.

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Qin Li, Jianfeng Lu, Weiran Sun. 2014-08-28. A convergent method for linear half-space kinetic equations. https://arxiv.org/abs/1408.6630

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