36 POTENTIAL PROBLEMS
Figure 2.4 Boundary elements: (a) constant;
(b) linear; (c) quadratic
considered are called 'nodes' and taken to be in the middle of each
segment for the so-called 'constant' elements (Figure 2.4(a)). These
are going to be the only elements considered in this section, but in the
next chapter we will also discuss the case of linear elements (i.e.
elements for which the nodes are at the intersection between elements
as shown in Figure 2.4(b)) and curved elements such as the quadratic
ones shown in Figure 2.4(c). For the latter case an extra mid-element
node is required and the elements are called quadratic.
For the constant element case the boundary is discretised into N
elements, of which N
are assumed to belong to Γ
values of u and q are assumed to be constant on each element and
equal to the values at the mid-node of the element. Note that on each