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

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [47 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02196242
Contributor : Alexandre Ern <>
Submitted on : Thursday, December 19, 2019 - 10:09:57 AM
Last modification on : Monday, January 13, 2020 - 1:18:23 AM

File

FEMwDG_HAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02196242, version 3
  • ARXIV : 1907.12605

Collections

Citation

Victor Calo, Alexandre Ern, Ignacio Muga, Sergio Rojas. An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms. 2019. ⟨hal-02196242v3⟩

Share

Metrics

Record views

15

Files downloads

25