Name
Title | ||
|---|---|---|
A Boundary Functional for the Least-Squares Finite- Element Solution of Neutron Transport Problems |
Abstract | ||
|---|---|---|
The least-squares finite-element framework for the neutron transport equation is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. This approach is extended by incorporating the boundary conditions into the least-squares functional. The proof of the V-ellipticity and continuity of the new functional leads to bounds of the discretization error for different regimes. For a P1 approximation of the angular dependence the resulting system of partial differential equations for the moments is explicitly derived. In the diffusion limit this system is essentially a Poisson equation for the zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. The use of these bounds is demonstrated in numerical examples for a spatial discretization using trilinear finite elements on a uniform tessellation into cubes. |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1137/S0036142998344706 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
boltzmann equation,posteriori error bound,least-squares approach,boundary functional,neutron transport equation,poisson equation,partial differential equation,finite-element discretization,element solution,resulting system,spatial discretization,least-squares finite-element framework,discretization error,neutron transport problems,least-squares variational formu- lation,pn approximation,least-squares finite,new functional lead,boundary condition,least square,transport equation,finite element,transportation problem | Discretization,Neutron transport,Boundary value problem,Mathematical optimization,Poisson's equation,Mathematical analysis,Finite element method,Partial differential equation,Diffusion equation,Mathematics,Laplace operator | Journal |
Volume | Issue | ISSN |
37 | 2 | 0036-1429 |
Citations | PageRank | References |
9 | 1.77 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thomas A. Manteuffel | 1 | 349 | 53.64 |
| Klaus J. Ressel | 2 | 22 | 3.32 |
| Gerhard Starke | 3 | 125 | 27.04 |