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

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  • Ahmed, Naveed
  • John, Volker
  • Matthies, Gunar
  • Novo, Julia

Abstract

A local projection stabilization (LPS) method in space is considered to approximate the evolutionary Oseen equations. Optimal error bounds with constants independent of the viscosity parameter are obtained in the continuous-in-time case for both the velocity and pressure approximation. 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.

Suggested Citation

  • Ahmed, Naveed & John, Volker & Matthies, Gunar & Novo, Julia, 2018. "A local projection stabilization/continuous Galerkin–Petrov method for incompressible flow problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 304-324.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:304-324
    DOI: 10.1016/j.amc.2018.03.088
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