Finite Element Analysis. Barna Szabó
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Numerical example
Letting
(1.173)
Table 1.7 The computed values of
| γ | 10−3 | 10−6 | 10−9 | 10−12 | 10−15 |
|---|---|---|---|---|---|
| u(ℓ) | 0.2540348 | 0.2500004 | 0.25(0)64 | 0.25(0)94 | 0.25(0)124 |
where p is the polynomial degree. Therefore
Referring to eq. (1.172), the coefficient matrix is modified by the application of Nitsche's method. Those modifications in the present case are:
The unconstrained right hand side vector without the modifications of Nitsche is:
and with the modifications of Nitsche it is:
The numerical results shown in Table 1.7 indicate that the stabilized formulation is remarkably robust. The notation
Notes
1 1 Ludwig Prandtl 1875–1953.
2 2 The generalized form is also called variational form or weak form.
3 3 The term “discretization” refers to processes by which approximating functions are defined. The most widely used discretizations will be described and illustrated by examples in this and subsequent chapters.
4 4 See Definition A.5 in the appendix.
5 5 Peter Gustav Lejeune Dirichlet 1805–1859.
6 6 Carl Gottfried Neumann 1832–1925.
7 7 Victor Gustave Robin (1855–1897).
8 8 A functional is a real‐valued function defined on a space of functions or vectors.