Discontinuous Least-Squares Spatial Discretization Schemes for the One-Dimensional Slab-Geometry Sn Equations Academic Article uri icon

abstract

  • We derive three new linear-discontinuous least-squares discretizations for the S n equations in one-dimensional slab geometry. Standard least-squares methods are not compatible with discontinuous trial spaces, and they are also generally not conservative. Our new methods are unique in that they are based upon a least-squares minimization principle, use a discontinuous trial space, are conservative, and retain the structure of standard Sn spatial discretization schemes. To our knowledge, conservative leastsquares spatial discretization schemes have not previously been developed for the S n equations. We compare our new methods both theoretically and numerically to the linear-discontinuous Galerkin method and the lumped linear-discontinuous Galerkin method. We find that one of our schemes is clearly superior to the other two and offers certain advantages over both of the Galerkin schemes.

author list (cited authors)

  • Zhu, L., & Morel, J. E.

citation count

  • 0

publication date

  • March 2010