Global Error Bounds for the Petrov-Galerkin Discretization of the Neutron Transport Equation

PDF Version Also Available for Download.

Description

In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L{sup 2} norm at the rate of h{sup 2}. Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it ... continued below

Physical Description

PDF-file: 23 pages; size: 0.3 Mbytes

Creation Information

Chang, B; Brown, P; Greenbaum, A & Machorro, E January 21, 2005.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L{sup 2} norm at the rate of h{sup 2}. Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it takes a neutron to cross the domain in a straight line. A consequence of this bound is that the global error of the Petrov-Galerkin approximation is of the same order of h as the local truncation error. We use this result to explain the widely held observation that the solution of the Petrov-Galerkin method is second accurate for one class of problems, but is only first order accurate for another class of problems.

Physical Description

PDF-file: 23 pages; size: 0.3 Mbytes

Source

  • Presented at: Nuclear Explosive Code Design Conference, Livermore , CA, United States, Oct 04 - Oct 07, 2004

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: UCRL-PROC-209167
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 917492
  • Archival Resource Key: ark:/67531/metadc889434

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • January 21, 2005

Added to The UNT Digital Library

  • Sept. 22, 2016, 2:13 a.m.

Description Last Updated

  • Dec. 5, 2016, 6:26 p.m.

Usage Statistics

When was this article last used?

Congratulations! It looks like you are the first person to view this item online.

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Chang, B; Brown, P; Greenbaum, A & Machorro, E. Global Error Bounds for the Petrov-Galerkin Discretization of the Neutron Transport Equation, article, January 21, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc889434/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.