Barycentric Coordinate Based Mixed Finite Elements on Quadrilateral/Hexahedral Mesh

Abstract

This paper presents barycentric coordinate interpolation reformulated as bilinear and trilinear mixed finite elements on quadrilateral and hexahedral meshes. The new finite element space is a subspace of H(div). Barycentric coordinate interpolations of discrete vector field with node values are also known as the corner velocity interpolation. The benefit of this velocity interpolation is that it contains the constant vector fields (uniform flow). We provide edge based basis functions ensuring the same interpolation, and show how these basis functions perform as separate velocity elements.