href="#fb3_img_img_2b124794-33bf-5667-9326-97cafe346799.png" alt="Graph depicts typical finite element basis functions in one dimension."/>
Figure 1.5 Typical finite element basis functions in one dimension.
Table 1.1 Local and global numbering in Example 1.6.
| Element number | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Numbering | 1 | 2 | 3 | ||||||
| local | 1 | 2 | 3 | 1 | 2 | 1 | 2 | 3 | 4 |
| global | 1 | 2 | 5 | 2 | 3 | 3 | 4 | 6 | 7 |
Each basis function is assigned a unique number, called a global number, and this number is associated with those element numbers and the shape function numbers from which the basis function is composed. The global and local numbers in this example are indicated in Table 1.1.
We denote
where the elements within the brackets are in the local numbering system whereas the coefficients aj and bi outside of the brackets are in the global system. The superscripts indicate the element numbers. The terms multiplied by
Assuming that the boundary conditions do not include Dirichlet conditions, the bilinear form can be written in terms of the
(1.76)
The treatment of Dirichlet conditions will be discussed separately in the next section.
The assembly of the right hand side vector from the element‐level right hand side vectors is analogous to the procedure just described. Referring to eq. (1.73) we write
