SOME GEOMETRICAL RESULTS AND ESTIMATES FOR QUADRILATERAL FINITE-ELEMENTS

The concept of the equivalent parallelogram associated with a quadrilateral is introduced. The quadrilateral may be regarded as-a perturbation of this parallelogram, which is most conveniently described by making use of properties of the isoparametric map which defines the quadrilateral. The equivalent parallelogram generates a natural means of defining a regular family of quadrilaterals; this definition is used together with other properties to obtain in a relatively simple manner estimates, inappropriate seminorms or norms, of the isoparametric map and its Jacobian, for use in the determination of finite element interpolation error estimates.