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arXiv · 2301.00285

On the Smoothness of the Solution to the Two-Dimensional Radiation Transfer Equation

Dean Wang
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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.

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Dean Wang. 2022-12-31. On the Smoothness of the Solution to the Two-Dimensional Radiation Transfer Equation. https://arxiv.org/abs/2301.00285

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