A weak Galerkin finite element method for the Navier–Stokes equations

• Published in: Journal of computational and applied mathematics Vol. 362; no. C; pp. 614 - 625
• Main Authors: Hu, Xiaozhe, Mu, Lin, Ye, Xiu
• Format: Journal Article
• Language: English
• Published: Belgium Elsevier B.V 15.12.2019; Elsevier
• Subjects: Finite element methods; Polyhedral meshes; The Navier–Stokes equations; Weak Galerkin; Weak Galerkin; Finite element methods; The Navier–Stokes equations; Polyhedral meshes
• ISSN: 0377-0427; 1879-1778; 1879-1778
• DOI: 10.1016/j.cam.2018.08.022

This paper introduces a weak Galerkin (WG) finite element method for the Navier–Stokes equations in the primal velocity–pressure formulation. Optimal-order error estimates are established for the corresponding numerical approximations. It must be emphasized that the WG finite element method is designed on finite element partitions consisting of arbitrary shape of polygons or polyhedra which are shape regular. Numerical experiments are presented to support the theoretical results.