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

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

doi:10.1016/j.apnum.2017.01.021

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

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Abstract

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:

Chaudhry, Jehanzeb H. ^[1]; Collins, J. B. ^[2]; Shadid, John N. ^[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. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Sun Feb 05 00:00:00 EST 2017

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1371472

Alternate Identifier(s):: OSTI ID: 1397844

Report Number(s):: SAND-2015-9789J
Journal ID: ISSN 0168-9274; PII: S0168927417300363

Grant/Contract Number:: AC04-94AL85000; FY2016

Resource Type:: Accepted Manuscript

Journal Name:: Applied Numerical Mathematics

Additional Journal Information:: Journal Volume: 117; Journal Issue: C; Journal ID: ISSN 0168-9274

Publisher:: Elsevier

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

Citation Formats


                    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., 2017. 
Web.  doi:10.1016/j.apnum.2017.01.021.

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                    Chaudhry, Jehanzeb H., Collins, J. B., & Shadid, John N. A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes.  United States.  https://doi.org/10.1016/j.apnum.2017.01.021

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                    Chaudhry, Jehanzeb H., Collins, J. B., and Shadid, John N. Sun .  
"A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes".  United States.  https://doi.org/10.1016/j.apnum.2017.01.021.  https://www.osti.gov/servlets/purl/1371472.

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@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         = {Sun Feb 05 00:00:00 EST 2017},

  month        = {Sun Feb 05 00:00:00 EST 2017}

}

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