PreprintCC BY 4.0HAL
Convergence analysis of moment-based approximations in kinetic theory
Abstract
As for Galerkin approximations, the method of moments consists in reducing the number of test functions in a variational approach to a finite number, then performing an approximation of the solution such that the resulting reduced problem is well-posed. It is commonly used in kinetic theory, relying on physical considerations, but few error estimates are available in the literature. This paper provides a functional framework adapted to study the convergence of these methods. Its use is illustrated for the convergence study of a vector of moments toward a kinetic distribution, pointwise, on a homogeneous time-dependent problem, and on a 1D-1V problem.
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BibTeX
@misc{pichard2026convergence,
title = {{Convergence analysis of moment-based approximations in kinetic theory}},
author = {Teddy Pichard},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05736689v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Convergence analysis of moment-based approximations in kinetic theory
AU - Teddy Pichard
PY - 2026
DA - 2026/09/03
PB - HAL
UR - https://hal.science/hal-05736689v1
AB - As for Galerkin approximations, the method of moments consists in reducing the number of test functions in a variational approach to a finite number, then performing an approximation of the solution such that the resulting reduced problem is well-posed. It is commonly used in kinetic theory, relying on physical considerations, but few error estimates are available in the literature. This paper provides a functional framework adapted to study the convergence of these methods. Its use is illustrated for the convergence study of a vector of moments toward a kinetic distribution, pointwise, on a homogeneous time-dependent problem, and on a 1D-1V problem.
ER -