Finite Element Solutions of Second-Order Forms of the Transport Equation at the Interface Between Diffusive and Non-diffusive Regions

June 1, 2001

Conference Paper

Finite Element Solutions of Second-Order Forms of the Transport Equation at the Interface Between Diffusive and Non-diffusive Regions

Abstract

We analyze the behavior of even- and odd-parity finite element discretizations of the transport equation at the boundary betweeen a diffusive and non-diffusive region in slab geometry. We find that the parity solutions each satisfy interface conditions that may not be accurate, but that their average should be extremely accurate. We also discuss the relationship between the even- and odd-parity equations and the self-adjoint angular flux equation. We conclude with numerical results that support our analysis results.

Revised: February 22, 2012 | Published: June 1, 2001

Citation

Gesh C.J., and M.L. Adams. 2001. Finite Element Solutions of Second-Order Forms of the Transport Equation at the Interface Between Diffusive and Non-diffusive Regions. In Proceedings of the International Meeting on Mathematical Methods for Nuclear Applications (M&C 2001), September 2001, Salt Lake City, Utah. La Grange Park, Illinois:American Nuclear Society. PNNL-SA-34520.