Exact(14)
In this section, we present some numerical results showing the validity of the approximation scheme and discuss the approximate velocity profile.
Furthermore, a new approximate velocity can be obtained by an element-by-element postprocessing which converges with order k+2 in the L2-norm.
The approximate velocity relation is accurate within 4% for the film thicknesses up to 20% of the acoustic wavelength in the polymer film, and is useful for analyzing the mass loading, swelling and viscoelastic effects in SAW vapor sensors.
The experiments were successfully modeled, without adjustable parameters, by means of a finite-difference numerical reservoir simulator and by computations based on an approximate velocity field given by a complex variable solution of the Laplace equation.
And third, it displays superconvergence properties that allow us to use the above-mentioned optimal convergence properties to define an element-by-element postprocessing scheme to compute a new and better approximate velocity.
In addition, all the approximate variables (including the approximate velocity and gradient) converge with the optimal order of k + 1 in the L2-norm, when polynomials of degree k ⩾ 0 are used to represent the numerical solution and when the time-stepping method is accurate with order k + 1.
Similar(46)
Four interaction phases (i.e., initial contact, loading with approximate velocities, unloading and free vibration) are clearly identified for the overall flexural failure of the pile-supported structures.
A comparison with results for no-shear plug flow reveals the relatively minor effects of shear (so that the approximating velocity profile produces only trivial error).
Least-squares spectral element solution of steady, two-dimensional, incompressible flows are obtained by approximating velocity, pressure and vorticity variable set on Gauss Lobatto Legendre nodes.
Algorithm 1 describes the proposed sequential process for identifying quasilinear motions in agents' dynamics and approximating velocity fields from them.
Figure 3 shows the proposed parametric function (vec {G}_{near}(r)) for approximating velocity fields in a near range of interactions over a two-dimensional plane (x,y).
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