skip to main content

DOE PAGESDOE PAGES

Title: A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error in a quantity-of-interest.
Authors:
 [1] ;  [2] ;  [3]
  1. The Univ. of New Mexico, Albuquerque, NM (United States)
  2. West Texa A&M Univ., Canyon, TX (United States)
  3. The Univ. of New Mexico, Albuquerque, NM (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
SAND-2015-9789J
Journal ID: ISSN 0168-9274; PII: S0168927417300363
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Applied Numerical Mathematics
Additional Journal Information:
Journal Volume: 117; Journal Issue: C; Journal ID: ISSN 0168-9274
Publisher:
Elsevier
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; a posteriori error estimation; adjoint operator; implicit–explicit schemes; IMEX schemes; Runge–Kutta schemes; multi-stage methods
OSTI Identifier:
1371472
Alternate Identifier(s):
OSTI ID: 1397844

Chaudhry, Jehanzeb H., Collins, J. B., and Shadid, John N.. A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes. United States: N. p., Web. doi:10.1016/j.apnum.2017.01.021.
Chaudhry, Jehanzeb H., Collins, J. B., & Shadid, John N.. A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes. United States. doi:10.1016/j.apnum.2017.01.021.
Chaudhry, Jehanzeb H., Collins, J. B., and Shadid, John N.. 2017. "A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes". United States. doi:10.1016/j.apnum.2017.01.021. https://www.osti.gov/servlets/purl/1371472.
@article{osti_1371472,
title = {A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes},
author = {Chaudhry, Jehanzeb H. and Collins, J. B. and Shadid, John N.},
abstractNote = {Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error in a quantity-of-interest.},
doi = {10.1016/j.apnum.2017.01.021},
journal = {Applied Numerical Mathematics},
number = C,
volume = 117,
place = {United States},
year = {2017},
month = {2}
}