Statistical riemann problems and a composition law for errors in numerical solutions of shock physics problems

James Glimm, John W. Grove, Yonghee Kang, Taewon Lee, Xiaolin Li, David H. Sharp, Yan Yu, Qian K. Ye, Ming Zhao

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We seek error models for shock physics simulations that are robust and understandable. The purpose of this paper is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones. We illustrate this idea in a simple context. This paper employs several simplifying assumptions (restriction to one spatial dimension, use of a simplified (gamma law) equation of state, and consideration of a single numerical method). In separate papers we will address the effect of these assumptions.

Original languageEnglish (US)
Pages (from-to)666-697
Number of pages32
JournalSIAM Journal on Scientific Computing
Volume26
Issue number2
DOIs
StatePublished - 2005
Externally publishedYes

Fingerprint

Shock
Cauchy Problem
Physics
Numerical Solution
Error Model
Chemical analysis
Equation of State
Error Estimates
Numerical Methods
Composite
Restriction
Equations of state
Numerical methods
Simulation
Composite materials
Context

Keywords

  • Composition law
  • Error model
  • Riemann problem
  • Uncertainty quantification

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Statistical riemann problems and a composition law for errors in numerical solutions of shock physics problems. / Glimm, James; Grove, John W.; Kang, Yonghee; Lee, Taewon; Li, Xiaolin; Sharp, David H.; Yu, Yan; Ye, Qian K.; Zhao, Ming.

In: SIAM Journal on Scientific Computing, Vol. 26, No. 2, 2005, p. 666-697.

Research output: Contribution to journalArticle

Glimm, James ; Grove, John W. ; Kang, Yonghee ; Lee, Taewon ; Li, Xiaolin ; Sharp, David H. ; Yu, Yan ; Ye, Qian K. ; Zhao, Ming. / Statistical riemann problems and a composition law for errors in numerical solutions of shock physics problems. In: SIAM Journal on Scientific Computing. 2005 ; Vol. 26, No. 2. pp. 666-697.
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