Finite Element Analysis. Barna Szabó
are finite. Therefore
(1.108)
In the special case when α is an integer and
Exercise 1.19 Show how eq. (1.106) is obtained from eq. (1.105). Provide details.
Example 1.10 Let us consider model problems in the form of eq. (1.103) with the following data:
With the information provided in Tables 1.2 and 1.3 it is possible to compare the estimated and exact values of the relative error. For example, using eq. (1.100) and
Table 1.3 Example: Computed and estimated values of the potential energy
. Uniform mesh refinement,
|
N |
|
|
|
|
---|---|---|---|---|---|
10 | 19 | −2.17753673 | −1.73038992 | −1.41382648 | −1.17955239 |
100 | 199 | −2.25079984 | −1.74673700 | −1.41675042 | −1.17984996 |
1000 | 1999 | −2.29589857 | −1.75303348 | −1.41745363 | −1.17989453 |
|
−2.37254083 | −1.75716094 | −1.41768637 | −1.17990276 |
the estimated relative error in energy norm for