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We address the following questions: (a) How does the error in energy norm depend on the parameter α, the mesh Δ and the p‐distribution p? and (b) How is this error distributed among the elements? Understanding these relationships is necessary for making sound choices of discretization based on a priori information concerning the regularity of the exact solution.
We compute the potential energy of the difference between the exact solution and its linear interpolant for the kth element:
The exact solution for
To obtain the potential energy of the difference between the exact solution and its linear interpolant for the kth element, denoted by
(1.124)
Figure 1.12 The exact solution for
The solution is
(1.125)
Using eq. (1.106) we get
(1.126)
where
(1.127)
and compute
Referring to Theorem 1.5, the error in energy norm associated with the kth element is
and the relative error in energy norm associated with the kth element is:
