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Solution of Incompressible Flow Equations by a High-Order Term-by-Term Stabilized Method

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Tomás Chacón Rebollo

    (Universidad de Sevilla. Facultad de Matemáticas. C/ Tarfia, Dpto. de Ecuaciones Diferenciales y Análisis Numérico)

  • Macarena Gómez Mármol

    (Universidad de Sevilla. Facultad de Matemáticas. C/ Tarfia, Dpto. de Ecuaciones Diferenciales y Análisis Numérico)

  • Isabel Sánchez Muñoz

    (Escuela Universitaria de Ingeniería Técnica de Agrícola, Dpto. de Matemática Aplicada I)

Abstract

This paper introduces a high-order easy-to-implement stabilized method for the numerical solution of convection-diffusion and incompressible flows. We obtain stable discretizations of equal-order interpolation of velocity and pressure, as is usual for stabilized methods. The penalty terms have a projection structure that allows to obtain a high order method. We present stability analysis and error estimates results for Oseen equations with Neumann boundary data with general Finite Element discretizations, and for Dirichlet boundary data with P2–P2 discretization and P1 projection. We also present some numerical tests that confirm the theoretical expectations.

Suggested Citation

  • Tomás Chacón Rebollo & Macarena Gómez Mármol & Isabel Sánchez Muñoz, 2010. "Solution of Incompressible Flow Equations by a High-Order Term-by-Term Stabilized Method," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 253-260, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_26
    DOI: 10.1007/978-3-642-11795-4_26
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