  Accuracy of a simulation is strongly depend on the grid quality. Here,
quality means orthogonality at the boundaries and quasi-orthogonality within
the critical regions, smoothness, bounded aspect ratios, solution adaptive
behaviour, etc. We review various functionals for generating high quality
structured quadrilateral meshes in two dimensional domains. Analysis of Winslow
and Modified Liao functionals are presented. Numerical examples are also
presented to support our theoretical analysis. We will demonstrate the use of
the Area functional for generating adaptive quadrilateral meshes.
