ABSTRACT
This chapter investigates the subject of element mapping. It was shown that distorted element configurations, such as those necessitated by the discretization of curved boundaries, can be realized by mapping simple parent domains into these configurations. When parent element domains are parametrically mapped into distorted configurations, care must be taken to avoid non-unique mappings. In such mappings, the one-to-one relationship between natural and global coordinates ceases to exist. Mathematically, non-unique mappings are characterized by a change in sign of the determinant of the Jacobian matrix. The chapter presents some specific measures of element distortion, along with guidelines that help avoid overly distorted elements. When parent element domains are parametrically mapped into distorted configurations, care must be taken to avoid non-unique mappings. In such mappings, the one-to-one relationship between natural and global coordinates ceases to exist. Mathematically, non-unique mappings are characterized by a change in sign of the Jacobian determinant.
