Residual estimates for post-processors in elliptic problems

Andreas Dedner, Jan Giesselmann, Tristan Pryer, Jennifer K. Ryan

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that “tweaks” a wide variety of existing post-processing techniques to enable efficient and reliable a posteriori bounds to be proven. This ultimately results in optimal error control for all manner of reconstruction operators, including those that superconverge. We showcase our results by applying them to two classes of very popular reconstruction operators, the Smoothness-Increasing Accuracy-Conserving filter and superconvergent patch recovery. Extensive numerical tests are conducted that confirm our analytic findings.
Original languageEnglish
Article number34
JournalJournal of Scientific Computing
Volume88
Issue number2
DOIs
Publication statusPublished - 21 Jun 2021

Keywords

  • A posteriori error bound
  • Adaptivity
  • Discontinuous Galerkin
  • Finite element method
  • Post-processing
  • SIAC filter
  • Superconvergent patch recovery

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