Rodolfo Araya, Abner Poza, Frederic Valentin:
A low-order local projection method for the incompressible Navier-Stokes equations in two and three dimensions
This work proposes and analyzes a new Local Projection Stabilized finite element method (LPS for short) for the non-linear incompressible Navier-Stokes equations. Stokes problems defined element-wisely drive the construction of the stabilized terms which make the present method stable for continuous velocity and (dis)continuous pressure finite element pairs P1 x Pk, k = 0,1, in two and three dimensions. Existence and uniqueness of a discrete solution and a non-singular branch of solutions are proved under standard assumptions. Also, we establish that the LPS method achieves optimal error estimates in the natural norms. Numerics assess the theoretical results and validate the LPS method in the three-dimensional case.
This preprint gave rise to the following definitive publication(s):
Rodolfo ARAYA, Abner POZA, Frederic VALENTIN: A low-order local projection method for the incompressible Navier-Stokes equations in two and three dimensions. IMA Journal of Numerical Analysis, vol. 36, 1, pp. 267-295, (2016).