Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering
Journal Article
·
· Mathematics of Computation
- California State University, Bakersfield, CA (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Here 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 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.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1838952
- Journal Information:
- Mathematics of Computation, Journal Name: Mathematics of Computation Journal Issue: 332 Vol. 90; ISSN 0025-5718
- Publisher:
- American Mathematical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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