Adjoint Error Estimation for Linear Advection

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An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The ... continued below

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PDF-file: 65 pages; size: 0.4 Mbytes

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Connors, J M; Banks, J W; Hittinger, J A & Woodward, C S March 30, 2011.

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An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.

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PDF-file: 65 pages; size: 0.4 Mbytes

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  • Report No.: LLNL-TR-477651
  • Grant Number: W-7405-ENG-48
  • DOI: 10.2172/1022148 | External Link
  • Office of Scientific & Technical Information Report Number: 1022148
  • Archival Resource Key: ark:/67531/metadc830491

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  • March 30, 2011

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

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  • Nov. 22, 2016, 3:54 p.m.

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Connors, J M; Banks, J W; Hittinger, J A & Woodward, C S. Adjoint Error Estimation for Linear Advection, report, March 30, 2011; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc830491/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.