Abstract
We present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter ε which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.
| Original language | English |
|---|---|
| Pages (from-to) | 2645-2669 |
| Number of pages | 25 |
| Journal | Mathematics of Computation |
| Volume | 90 |
| Issue number | 332 |
| DOIs | |
| State | Published - 2021 |
Funding
This material was based, in part, upon work supported by the DOE Office of Advanced Scientific Computing Research and by the National Science Foundation under Grant No. 1217170. ORNL is operated by UT-Battelle, LLC., for the U.S. Department of Energy under Contract DE-AC05-00OR22725. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
Keywords
- Radiative transfer equation
- asymptotic preserving
- convergence analysis
- discontinuous Galerkin
- discrete-ordinate