A comparison of various mixed-interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations

Abstract

Abstract It is generally recognized that mixed interpolation should be used in the velocity-pressure finite element formulation of incompressible viscous flow problems. In this paper, four types of mixed interpolation elements are considered and compared. These are namely: six-node triangular elements, eight-node serendipity elements, nine-node Lagrangian elements and four-node quadrilateral elements. The comparison is made via two numerical examples concerning steady flow through a sudden expansion and steady free thermal convection in a square cavity. Results indicate that for the same number of pressure unknowns, serendipity elements can give considerably less accurate pressure fields than most other types of elements. Lagrangian elements give the most accurate pressure and velocity distributions. The numerical performance of triangular elements is intermediate in accuracy and is dependent on the triangular pattern used. Finally, the four-node element may generate spurious pressure modes depending on the boundary condition specifications.