Diffusion asymptotics for linear transport with low regularity

Article type: Research Article

Authors: Egger, Herbert | Schlottbom, Matthias^;

Affiliations: Numerical Analysis and Scientific Computing, Department of Mathematics, TU Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany. Emails: {egger, schlottbom}@mathematik.tu-darmstadt.de

Note: [] Corresponding author. E-mail: [email protected]

Abstract: We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of the solution in the L2 norm is established without artificial regularity requirements. This is important to be able to deal with problems involving realistic geometries and heterogeneous media. In a second step we prove the usual O(ε) convergence rates under very mild additional assumptions. The generalization of the results to convergence in Lp with p≠2 and some limitations are discussed.

Keywords: radiative transfer, neutron transport, diffusion limit, asymptotic analysis

DOI: 10.3233/ASY-141235

Journal: Asymptotic Analysis, vol. 89, no. 3-4, pp. 365-377, 2014