Conditions for the invertibility of the isoparametric mapping for hexahedral finite elements

We consider the isoparametric mapping, which maps a given reference element onto a global element given by its vertices, for trilinear finite elements on hexahedra. We present an algorithm that checks the positivity of the Jacobian determinant depending on the position of the vertices and therefore ensures that the isoparametric mapping is locally invertible. (C) 2002 Elsevier B.V. All rights reserved.