A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

Yalchin R. Efendiev, Raytcho D. Lazarov, Minam Moon, Ke Shi

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.
Original languageEnglish (US)
Pages (from-to)243-256
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Volume292
DOIs
StatePublished - Oct 22 2014

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications

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