Multilinear Jacobians for isoparametric planar elements

摘要

A systematic procedure is developed for analysing the Jacobians of planar finite elements. Conditions are derived for the Jacobians to be linear or multilinear in the two isoparametric coordinates. For the case of the 6-noded triangle a complete geometrical description is given of elements which have a positive linear or quadratic Jacobian. Some partial geometrical results are also given for the eight-noded quadrilateral and the cubic triangle. Numerical examples involving the solution of Laplace's equation compare results obtained by using exactly and non-exactly integrable elements near curved boundaries.