We will be concerned with evaluation of the integral
Defining:
(1.68)
the following expression is obtained:
(1.69)
where , and
The terms of the coefficient matrix are computable from the mapping, the definition of the shape functions and the function . The matrix is called the element‐level Gram matrix13 or the element‐level mass matrix. Observe that is symmetric. In the important special case where is constant on Ik it is possible to compute once and for all. This is illustrated by the following example.
Example 1.4 When is constant on Ik and the Legendre shape functions are used then the element‐level Gram matrix is strongly diagonal. For example, for the Gram matrix is:
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