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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