Difference between tetrahedral and hexahedral element mesh
Answers
Tetrahedral elements can fit better complex geometry. However, when you integrate the shape functions with points of Gauss it is less accurate than hexahedral elements. In addition, one of the factors that determines the quality of your mesh is the distortion of your elements. The reason for this lays on the mapping from real to natural space of integration. To sum up, if your geometry is simple, the best option is to mesh it with hexahedral elements. If it is not possible (curved geometries, accute angles or similar) then go with tetrahedal but controlling the distortion of the elements.
Hexahedra meshes are economic with the number of elements because the same degrees of freedom (or for 8 nodes) for one Hexaedron corresponds to six Tetrahedra. It is obvious that increasing the number of elements will not increase the size of the global finite element matrices but the computations for one hexahedron are generated also for six tetrahedra.