Sentence examples for finite element estimates from inspiring English sources

It is shown that the quick Voigt (constant strain) orientation averaging procedure gives excellent viscoelastic stiffness predictions provided that the finite element estimates are used for the required moduli of the basis FOD state with fully aligned fibers.

The obtained finite element estimates were compared with predictions of the generalized self-consistent (GSC) model (Christensen and Lo, 1979) and it was shown that the model was accurate over the entire range of practically relevant sphere fractions.

A posteriori error estimates and adaptive finite element approximation for parameter estimation problems have been obtained in [7, 8].

Although a priori error estimates and a posteriori error estimates of finite element approximation are widely used in numerical simulations, they have not yet been utilized in nonlinear parabolic boundary optimal control problems.

This chapter presents the discretization error of the finite element approximation and a posteriori estimates of such error.

Furthermore their finite element approximation and a priori error estimates were established long ago, for example, see [1] [7], [9].

It is based on Nakao's method by using finite element approximation and its explicit error estimates for the problem.

Next, a posteriori error estimates of mixed finite element approximation for the control problem are given in Section 3.

Then the a priori error estimates for its finite element approximation are obtained with the optimal convergence order.

In Section 4, we establish the optimal a priori error estimates for the finite element approximation of the control problem.

The finite element model estimates the high-frequency modes that have significant tooth mesh deflection without considering the shafts and fixtures.