Sentence examples for be the interpolation operator from inspiring English sources

For (win U), let (Pi_{h}w) be the interpolation operator of w onto (U_{h}).

For (win U), let (Pi_{h}^w) be the interpolation operator of w onto the test space (tilde{U}_{h}), i.e., Pi_{h}^w=sum_{mathbf{z}in Z^{circ}_{h}}w( mathbf{z} phi_{z}.

Suppose (u,u_{t}in H^{3}(Omega),u_{tt}in H^{2}(Omega)) and (Pi_{h}) is the interpolation operator.

Let Π x y e be the linear interpolation operator with respect to ( x, y ) ∈ D, and let Π z e be the linear interpolation operator with respect to z ∈ L. Thus we may define the tensor-product linear interpolation operator by Π e : H 0 1 ( e ) → P ( e ).

Lemma 2.1 Let π ˆ h be the average interpolation operator defined in [22].

Let ({pi}_{h}) be the average interpolation operator defined in [24].

First, the overlapping grid method based on Lagrange interpolating polynomials is described and a theoretical analysis of the interpolation operator is then carried out.

The interpolation operator is expressed as (r_{i,j}=bar{r}_{bar{i},bar{j}}).

The interpolation operator (P_{j-1}^{j}) usually is of higher accuracy than the interpolation operator (I_{j-1}^{j}) used within the multigrid iteration.

The second term in (3.11), resulting from the replacement of the mixed elliptic projection by the interpolation operator, cannot be estimated straightforwardly by Hölder's inequality, (3.4) or the inverse inequality (3.5).

end{aligned} (Pi_{h}:H^{2}(Omega)rightarrow V_{h}) is the corresponding interpolation operator and define that ((cdot,cdot)_{h}=sum_{Tinmathcal {T}_{h}} (cdot,cdot)_{T},langlecdot,cdotrangle_{h}=sum_{Ein mathcal {E}_{h}} langlecdot,cdotrangle_{E}).