Anisotropic advancing front quadrangulation with optimization-based smoothing

Recent research in high-order discretisations of partial differential equations suggests the need for mesh adaptivity to reduce solution error at a reasonable computational cost [8]. Simplices are often used because of their ability to easily mesh complex domains; however, hexahedra offer better alignment with solution features, such as shocks or boundary layers. The goal of this report is to describe some work in developing an anisotropic quadrilateral mesh generator with the intent of extending the framework to higher dimensions.