Incorporating curvature to the boundary of linear and highorder meshes when a target geometry is unavailable

Barcelona Supercomputing Center In this work, two new methods are presented: first, a given linear tetrahedral volume mesh is refined in such a way that its boundary tends to an almost everywhere C^2-continuous surface, and second, a curved high-order tetrahedral mesh which boundary approximates an almost everywhere C^2 surface is generated from a linear tetrahedral mesh. The aim of these curved meshes is to provide an almost everywhere C^2 smooth parametrization of curved boundaries suitable for finite element analysis with unstructured high-order methods. To illustrate the applicability of the methods, several curved high-order volume meshes have been generated from linear meshes obtained by digitizing real volumes.