Orthogonality constrained gradient reconstruction for superconvergent linear functionals

Porcù, Roberto; Chiaramonte, Maurizio M.

doi:10.1007/s10543-019-00775-2

Title: Orthogonality constrained gradient reconstruction for superconvergent linear functionals

Journal Article · 05 January 2020 · BIT Numerical Mathematics

DOI: https://doi.org/10.1007/s10543-019-00775-2 · OSTI ID:1604723

Porcù, Roberto ^[1];

^[2]

Princeton Univ., NJ (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Facebook Reality Labs., Redmond, WA (United States); Princeton Univ., NJ (United States)

The post-processing of the solution of variational problems discretized with Galerkin finite element methods is particularly useful for the computation of quantities of interest. Such quantities are generally expressed as linear functionals of the solution and the error of their approximation is bounded by the error of the solution itself. Several a posteriori recovery procedures have been developed over the years to improve the accuracy of post-processed results. Nonetheless such recovery methods usually deteriorate the convergence properties of linear functionals of the solution and, as a consequence, of the quantities of interest as well. Finally, the paper develops an enhanced gradient recovery scheme able to both preserve the good qualities of the recovered gradient and increase the accuracy and the convergence rates of linear functionals of the solution.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1604723

Journal Information:: BIT Numerical Mathematics, Journal Name: BIT Numerical Mathematics Vol. 60; ISSN 0006-3835

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Barlow points
goal-oriented error estimation
linear functionals
quantities of interest
superconvergent patch recovery

Title: Orthogonality constrained gradient reconstruction for superconvergent linear functionals

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