Adaptive finite element simulation of incompressible flows by hybrid continuous-discontinuous Galerkin formulations

Santiago Badia, Joan Baiges

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on nonmatching element interfaces of nonconforming meshes. Then we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPG-type continuous Galerkin formulations and the jump stabilization of discontinuous Galerkin formulations. Optimal stability and convergence results are obtained. For the adaptive setting, we use a standard error estimator and marking strategy. Numerical experiments show the optimal accuracy of the hybrid algorithm for both uniformly and adaptively refined nonconforming meshes. The outcome of this work is a finite element formulation that can naturally be used on nonconforming meshes, as discontinuous Galerkin formulations, while keeping the much lower CPU cost of continuous Galerkin formulations.

Original languageEnglish
Pages (from-to)A491–A516
Number of pages26
JournalSIAM Journal on Scientific Computing
Volume35
Issue number1
DOIs
Publication statusPublished - 22 Apr 2013
Externally publishedYes

Keywords

  • Adaptive refinement
  • Continuous-discontinuous Galerkin
  • Equal-order interpolation
  • Incompressible flows
  • Stabilization

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