Analysis of the grad-div stabilization for the time-dependent Navier–Stokes equations with inf-sup stable finite elements

• Published in: Advances in computational mathematics Vol. 44; no. 1; pp. 195 - 225
• Main Authors: de Frutos, Javier, García-Archilla, Bosco, John, Volker, Novo, Julia
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2018; Springer Nature B.V
• Subjects: Compatibility; Computational fluid dynamics; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Finite element method; Fluid flow; Mathematical analysis; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Stabilization; Visualization; Error bounds independent of the viscosity; Nonlocal compatibility condition; Incompressible Navier–Stokes equations; 65M60; Inf-sup stable finite element methods; Backward Euler method; 65M12; Grad-div stabilization

This paper studies inf-sup stable finite element discretizations of the evolutionary Navier–Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and consequently has to satisfy nonlocal compatibility conditions as well a...