Interpolation with anisotropic quadrilateral elements
Anisotropic finite elements are characterized by more than one size parameter which can be chosen independently. Such elements can be used to approximate functions with certain directional features efficiently. Examples include boundary layers in singularly perturbed problems and edge singularities in various elliptic problems.
The discretization error analysis leads typically to the estimation of the interpolation errors. Such estimates are usually proven via a transformation to a reference element in order to separate the size parameters. This process must be done more carefully in the case of anisotropic elements in comparison with shape-regular elements. Some of the pitfalls and tricks are presented. The focus of the talk is on bilinear quadrilateral elements distinguishing the affine and isoparametric cases but higher order polynomials and hexahedral elements are commented. Other than Lagrangian elements are also shortly discussed.
