Smoothness-Increasing Accuracy-Conserving Filters for Discontinuous Galerkin Methods: Challenging the Assumptions of Symmetry and Uniformity

Xiaozhou Li

Research output: ThesisDissertation (TU Delft)


In this dissertation, we focus on exploiting superconvergence for discontinuous Galerkin methods and constructing a superconvergence extraction technique, in particular, Smoothness-Increasing Accuracy-Conserving (SIAC) filtering. The SIAC filtering technique is based on the superconvergence property of discontinuous Galerkin methods and aims to achieve a solution with higher accuracy order, reduced errors and improved smoothness.
The main contributions described in this dissertation are: 1) an efficient one-sided SIAC filter for both uniform and nonuniform meshes; 2) one-sided derivative SIAC filters for nonuniform meshes; 3) the theoretical and computational foundation for using SIAC filters for nonuniform meshes; and 4) the application of SIAC filters for streamline integration.
Original languageEnglish
Awarding Institution
  • Delft University of Technology
  • Vuik, C., Supervisor
  • Ryan, Jennifer, Advisor
Award date9 Jul 2015
Print ISBNs978-94-6186-500-7
Publication statusPublished - 2015


  • Discontinuous Galerkin method
  • post-processing
  • superconvergence
  • nonuniform meshes
  • SIAC filtering
  • boundaries

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