On the Smoothness of the Solution to the Two-Dimensional Radiation Transfer Equation
Analysis of PDEs
2023-11-10 v4 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
In this paper, we deal with the differential properties of the scalar flux defined over a two-dimensional bounded convex domain, as a solution to the integral radiation transfer equation. Estimates for the derivatives of the scalar flux near the boundary of the domain are given based on Vainikko's regularity theorem. A numerical example is presented to demonstrate the implication of the solution smoothness on the convergence behavior of the diamond difference method.
Keywords
Cite
@article{arxiv.2301.00285,
title = {On the Smoothness of the Solution to the Two-Dimensional Radiation Transfer Equation},
author = {Dean Wang},
journal= {arXiv preprint arXiv:2301.00285},
year = {2023}
}