Multivariant finite elements for three‐dimensional simulation of viscous incompressible flows

Within multivariant elements, which have restricted degrees of freedom at some nodes, different velocity components have different variations. Shape functions for the multivariant elements Q   1 +P o and R   2 +P o are developed. With such shape functions the value of a velocity component within a multivariant element is shown to depend upon all the independent components of velocity at the nodes of the element. The use of the Q 1 P 0 element to simulate flows with discontinuous boundary conditions generated disturbance throughout the flow domain, giving erroneous pressure and velocity distributions. The Q   1 +P o element restricted the disturbance due to such discontinuities to a small region near the singular points, whereas the P   2 +P o element completely eliminated the fluctuations. Flows with discontinuous boundary conditions were simulated with reasonable accuracy by partially relaxing the no‐slip condition on the Q 1 P o elements near the singular points.