Picture of a black hole

Strathclyde Open Access research that creates ripples...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of research papers by University of Strathclyde researchers, including by Strathclyde physicists involved in observing gravitational waves and black hole mergers as part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) - but also other internationally significant research from the Department of Physics. Discover why Strathclyde's physics research is making ripples...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Convergence analysis of a residual local projection method for the Navier-Stokes equation

Araya, Rodolfa and Barrenechea, Gabriel and Poza, A. and Valentin, Frédéric (2012) Convergence analysis of a residual local projection method for the Navier-Stokes equation. SIAM Journal on Numerical Analysis, 50 (2). pp. 669-699. ISSN 0036-1429

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

This work presents and analyzes a new residual local projection stabilized finite element method (RELP) for the nonlinear incompressible Navier–Stokes equations. Stokes problems defined elementwise drive the construction of the residual-based terms which make the present method stable for the finite element pairs $\mathbb{P}_1/\mathbb{P}_l$, $l=0,1$. Numerical upwinding is incorporated through an extra control on the advective derivative and on the residual of the divergence equation. Well-posedness of the discrete problem as well as optimal error estimates in natural norms are proved under standard assumptions. Next, a divergence-free velocity field is provided by a simple postprocessing of the computed velocity and pressure using the lowest order Raviart–Thomas basis functions. This updated velocity is proved to converge optimally to the exact solution. Numerics assess the theoretical results and validate the RELP method.