A family of H1 ‐conforming finite element spaces for calculations on 3D grids with pinch‐outs
Stephen Lincoln Lyons, Rossen R. Parashkevov, Xiaohui Wu · Numerical Linear Algebra with Applications · 2006
Abstract In this paper, we develop scalar nodal bases for a family of shapes that degenerate from hexahedra due to the merging of two neighbouring vertices on an edge with zero length, a phenomenon commonly referred to as ‘pinch‐out’. These nodal bases together with compatible mapping functions from the reference space to the physical space can be used to build H1 conforming, finite element spaces on meshes consisting of mixed elements with triangular and non‐planar quadrilateral faces. A novel feature in our constructions is the use of rational functions, whose first partial derivatives are uniformly bounded albeit discontinuous at isolated points. Properties of these bases and resulting finite element spaces are studied. Copyright © 2006 John Wiley & Sons, Ltd.