This paper is devoted to the construction of nonconforming finite elements for the discretization of fourth order elliptic partial differential operators in three spatial dimensions. The newly constructed elements include two nonconforming tetrahedral finite elements and one quasi-conforming tetrahedral element. These elements are proved to be convergent for a model biharmonic equation in three...

 The accuracy of finite element approximation on tetrahedral elements is studied using the previously derived maximum eigenvalue condition. This condition is linked with the minimum singular value of the element ‘edge shape matrix’ that characterizes the flatness of an element. A geometric interpretation of these results is discussed. From the theoretical viewpoint, a better insight into the m...

We present a preliminary method to generate polyhedral meshes of general non-manifold domains. The method is based on computing the dual of a general tetrahedral mesh. The resulting mesh respects the topology of the domain to the same extent as the input mesh. If the input tetrahedral mesh is Delaunay and well-centered, the resulting mesh is a Voronoi mesh with planar faces. For general tetrahe...

The issue of mesh quality for unstructured triangular and tetrahedral meshes is considered. The theoretical background to finite element methods is used to understand the basis of present-day geometrical mesh quality indicators. Simple tetrahedral mesh quality measures using both geometrical and solution information are described. Some of the issues in mesh quality for unstructured tetrahedral ...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

Abstract Mesh optimization is essential to enable sufficient element quality for numerical methods such as the finite method (FEM). Depending on required accuracy and geometric detail, a mesh with many elements necessary resolve small-scale details. Sequential of large meshes often imposes long run times. This especially an issue Delaunay-based methods. Recently, notion harmonic triangulations ...