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Stabilizing the ℙ1/ℙ0 Element for the Stokes Problem via Multiscale Enrichment

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Rodolfo Araya

    (Universidad de Concepción, Depto. de Ingeniería Matemática)

  • Gabriel R. Barrenechea

    (Universidad de Concepción, Depto. de Ingeniería Matemática)

  • Frédéric Valentin

    (Laboratório Nacional de Computação Científica)

Abstract

This work concerns the derivation of new stabilized finite element methods for the Stokes problem. Starting from pairs of spaces which are not stable, they are made stable by enriching them with multiscale functions, i.e., functions which are local, but not bubble-like, arising from the solution of local problems at the element level. This general methodology is applied to stabilize the non-stable ℙ1/ℙ0 pair.

Suggested Citation

  • Rodolfo Araya & Gabriel R. Barrenechea & Frédéric Valentin, 2006. "Stabilizing the ℙ1/ℙ0 Element for the Stokes Problem via Multiscale Enrichment," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 752-760, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_73
    DOI: 10.1007/978-3-540-34288-5_73
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