A posteriori error estimation for multistage 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 quantityofinterest for approximations obtained from multistage 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 adjointbased 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 quantityofinterest.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 The Univ. of New Mexico, Albuquerque, NM (United States)
 West Texa A&M Univ., Canyon, TX (United States)
 The Univ. of New Mexico, Albuquerque, NM (United States); Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Publication Date:
 Report Number(s):
 SAND20159789J
Journal ID: ISSN 01689274; PII: S0168927417300363
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Applied Numerical Mathematics
 Additional Journal Information:
 Journal Volume: 117; Journal Issue: C; Journal ID: ISSN 01689274
 Publisher:
 Elsevier
 Research Org:
 Sandia National Lab. (SNLNM), 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; multistage 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 multistage 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 multistage 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 multistage 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 multistage 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 quantityofinterest for approximations obtained from multistage 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 adjointbased 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 quantityofinterest.},
doi = {10.1016/j.apnum.2017.01.021},
journal = {Applied Numerical Mathematics},
number = C,
volume = 117,
place = {United States},
year = {2017},
month = {2}
}