Isoparametric Hermite elements

Abstract Isoparametric Hermite elements are created using Bogner–Fox–Schmit rectangles on a reference domain and mapping these numerically onto the computational domain. The difficulties involved in devising explicit C 1 shape functions for isoparametric elements are thus avoided, and the resulting elements have all the benefits of full C 1 continuity, the simplicity of the Bogner–Fox–Schmit element and the geometrical flexibility expected from higher‐order isoparametric elements. The numerical mapping consists in the finite element solution of a linear boundary value problem, which is inexpensive and is carried out as a preprocessing operation—the required derivatives of the mapping then being supplied to the main analysis as data. Some care is required in defining the differential boundary conditions, and guidance on this is provided. Examples are given showing the success of the mapping procedure, and the use of the resulting elements in the solution of some boundary value problems. The numerical results confirm a convergence analysis provided for the new isoparametric Hermite element.