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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/14046Collections
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Show full item recordScholars@Duke
Jianfeng Lu
Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm
development for problems from computational physics, theoretical chemistry, materials
science and other related fields.More specifically, his current research focuses include:Electronic
structure and many body problems; quantum molecular dynamics; multiscale modeling
and analysis; rare events and sampling techniques.

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