Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit
KAUST Grant NumberKUS-C1-016-04
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AbstractWe revisit some results from M. L. Adams [Nu cl. Sci. Engrg., 137 (2001), pp. 298- 333]. Using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous Galerkin approximation to converge to the correct limit solution in the diffusive regime is that the approximation space contains a linear space of continuous functions, and the restrictions of the functions of this space to each mesh cell contain the linear polynomials. Furthermore, the discrete diffusion limit converges in the Sobolev space H1 to the continuous one if the boundary data is isotropic. With anisotropic boundary data, a boundary layer occurs, and convergence holds in the broken Sobolev space H with s < 1/2 only © 2010 Society for Industrial and Applied Mathematics.
CitationGuermond J-L, Kanschat G (2010) Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit. SIAM J Numer Anal 48: 53–78. Available: http://dx.doi.org/10.1137/090746938.
SponsorsReceived by the editors January 20, 2009; accepted for publication (in revised form) December 21, 2009; published electronically April 2, 2010. This material is based upon work supported by the Department of Homeland Security under agreement 2008-DN-077-ARI018-02, National Science Foundation grants DMS-0713829, DMS-0810387, and CBET-0736202, and is partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).