Finite Element Analysis. Barna Szabó

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Letting in eq. (1.171) we get the stabilized method proposed by Nitsche [67]:

(1.172)

      Numerical example

      Letting , , and we construct the numerical problem using one element and the hierarchic shape functions defined in Section 1.3.1. By definition:

      (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 and and, using the Legendre shape functions, for the unconstrained coefficient matrix, without the modifications of Nitsche, is

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

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