A mixed variational framework for the radiative transfer equation. (English) Zbl 1247.65163
The paper is concerned with presenting a variational framework for the analysis and discretisaton of the radiative transfer equation. Results are provided on weak and strong solutions and a range of numerical methods is considered with particular focus on approximation using Galerkin methods and a finite element example.
The main contributions of the work, apart from the proposed variational framework, are the derivation of simple conditions for stability and quasi-optimal error estimates for Galerkin approximations, and a rigorous derivation of a second order form of the radiative transfer equation.
The main contributions of the work, apart from the proposed variational framework, are the derivation of simple conditions for stability and quasi-optimal error estimates for Galerkin approximations, and a rigorous derivation of a second order form of the radiative transfer equation.
Reviewer: Neville Ford (Chester)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45K05 | Integro-partial differential equations |
| 85A25 | Radiative transfer in astronomy and astrophysics |
| 78A40 | Waves and radiation in optics and electromagnetic theory |
Keywords:
radiative transfer equation; mixed variational methods; Galerkin methods; spherical harmonics; weak and strong solutions; finite element; stability; quasi-optimal error estimatesReferences:
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