chapter  3
20 Pages

3D hp Finite Element Method

The entire discussion on Galerkin method, calculation of element matrices, construction of FE (Finite Element) basis functions and the corresponding assembly procedure, incorporation of Dirichlet boundary conditions, and all other topics discussed in Volume I, remains valid in the three-dimensional (3D) case, and we shall not repeat it here. Instead, we shall point only to extra technical details and difficulties related inherently to 3D. We will start with a short discussion on construction of FE basis functions on 3D regular meshes and related details on the orientation of mid-edge and mid-face nodes. Next, we will present our 1-irregular meshes algorithm and its modification used in the automatic hp-adaptive strategy discussed in Chapter 6. Finally, we will outline the implementation of constrained approximation and the corresponding assembly procedure for elements with constrained (hanging) nodes.