A posteriori error analysis in radiative transfer

Abstract

The radiative transfer equation (RTE) arises in a wide variety of applications. In the literature, there has been much study of the RTE. The main purpose of the paper is to present a unified framework to develop a posteriori estimates for numerical solution errors and modeling errors, in an energy norm natural to the RTE problem. The derivation of the error estimates is through duality arguments. A posteriori error estimates in an norm are also presented, extending existing results available in the literature. The error estimates are completely computable in the sense that no unspecified constants are involved. A posteriori error estimates for numerical solutions are the basis for developing efficient adaptive solution algorithms, whereas a posteriori estimates for modeling errors are useful to analyze the effects of uncertainties in problem data on the solution.

Keywords:

• radiative transfer equation
• weak formulation
• variational principle
• dual formulation
• a posteriori error estimation
• parity equation

AMS Subject Classifications:

• 65N15
• 49S05

Acknowledgements

The work was supported by grants from the Simons Foundation. The author thanks the two anonymous referees for their valuable comments that lead to an improvement of the paper.