An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms

Victor M. Calo, Alexandre Ern, IGNACIO PATRICIO PEDRO MUGA URQUIZA, Sergio Rojas

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that has inf–sup stability. We formulate this residual minimization as a stable saddle-point problem, which delivers a stabilized discrete solution and a residual representation that drives the adaptive mesh refinement. Numerical results on an advection–reaction model problem show competitive error reduction rates when compared to discontinuous Galerkin methods on uniformly refined meshes and smooth solutions. Moreover, the technique leads to optimal decay rates for adaptive mesh refinement and solutions having sharp layers.

Original languageEnglish
Article number112891
JournalComputer Methods in Applied Mechanics and Engineering
Volume363
DOIs
StatePublished - 1 May 2020
Externally publishedYes

Keywords

  • Adaptive mesh refinement
  • Advection–reaction
  • Discontinuous Petrov–Galerkin
  • Inf–sup stability
  • Residual minimization
  • Stabilized finite elements

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