How can we approximate curves and meshes in the Hermite-Bezier framework ?

Abstract

The Bezier approximation is now well-established in CAD (Computer Aided Design). Conversely, the Hermite finite element produces a higher continuity approximation space. 

By combining these two strategies, we will derive a Hermite-Bezier approximation that will help to

• Capture smooth geometries with few finite elements.
• Accurately represent anisotropies arising in plasma physics.

Furthermore, cubic Hermite and other high-order solution spaces have convergence advantages in finite element simulations compared with linear solution spaces and give rise to continuous properties between elements. A proper mapping between the local and global finite element spaces ensures the continuity of field solutions in these finite element problems. We will provide the main steps of this construction in the context of a given parametric curve.