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The mixed formulations are numerically tested for both the uniform h- and p-extensions.

The mixed formulations are based on various generalizations of the so-called Ciarlet Raviart technique.

For the purpose of completeness, two one-dimensional mixed formulations are also analyzed.

The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces.

The proposed mixed formulations are based on generalizations of the well-known Ciarlet Raviart mixed method, where the new main variables are related to second-order (or fourth order, for the buckling problem) derivatives of the displacement field.

The advantages of mixed formulations are well known in that they simplify the form of the governing equations and can lead to potentially significant savings in computational effort for given accuracy.

Similar(54)

The most common of these mixed formulations is the Lagrange Multiplier (LM) method, a two-field variational approach which has been used widely to enforce incompressibility of the myocardium by introducing a variable to respresent the hydrostatic pressure [16,17,4,19,44].

For the linear track model, the results from the mixed formulation are in excellent agreement with those from a semi-analytical model formulated in the wavenumber-frequency domain, particularly in the vicinity of the loading point.

In particular, the global ¯¯¯B projection method and a mixed formulation are examined and compared, showing equivalently optimal convergence with regard to displacement solutions.

The mixed formulation is minimized in the sense of least-squares.

A mixed formulation is considered such that both pressure and velocity are approximated simultaneously.

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