WIAS Preprint No. 2347, (2016)

A local projection stabilization/continuous Galerkin--Petrov method for incompressible flow problems


Authors

  • Ahmed, Naveed
    ORCID: 0000-0002-9322-0373
  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Matthies, Gunar
  • Novo, Julia
    ORCID: 0000-0001-6667-5666

2010 Mathematics Subject Classification

  • 65M12 65M15 65M80

Keywords

  • Evolutionary Oseen problem, inf-sup stable pairs of finite element spaces, local projection stabilization (LPS) methods, continuous Galerkin--Petrov (cGP) methods

DOI

10.20347/WIAS.PREPRINT.2347

Abstract

The local projection stabilization (LPS) method in space is consid-ered to approximate the evolutionary Oseen equations. Optimal error bounds independent of the viscosity parameter are obtained in the continuous-in-time case for the approximations of both velocity and pressure. In addition, the fully discrete case in combination with higher order continuous Galerkin--Petrov (cGP) methods is studied. Error estimates of order k + 1 are proved, where k denotes the polynomial degree in time, assuming that the convective term is time-independent. Numerical results show that the predicted order is also achieved in the general case of time-dependent convective terms.

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