Baseline a Subscript j Baseline b Subscript i Baseline identical-to StartSet b EndSet Superscript upper T Baseline left-bracket upper K Superscript left-parenthesis k right-parenthesis Baseline right-bracket StartSet a EndSet period"/>
The terms of the stiffness matrix depend on the the mapping, the definition of the shape functions and the function . The matrix is called the element stiffness matrix. Observe that that is, is symmetric. This follows directly from the symmetry of and the fact that the same basis functions are used for un and vn.
In the finite element method the integrals are evaluated by numerical methods. Numerical integration is discussed in Appendix E. In the important special case when is constant on Ik, it is possible to compute once and for all. This is illustrated by the following example.
Example 1.3 When is constant on Ik and the Legendre shape functions are used then, with the exception of the first two rows and columns, the element stiffness matrix is perfectly diagonal:
