Spatial interpolation

Hong Y, Nix HA, Hutchinson MF, Booth TH (2005) Spatial interpolation of monthly mean climate data for China. Int J Climatol 25 1369-1379... 

Perform Savitsky-Golay smoothing with derivatives on individual spectra or entire image cubes Spatially interpolate... 

Use available explanatory data first before performing spatial interpolation. 

Spatial interpolation of geochemical data has greatly improved the quality of geochemical data presentation and subsequent interpretation over the past 20 years or so. 

The RSL, surfaces have to be determined by spatial interpolation of data from shoreline displacement curves (rsl e RSL,) reconstructed from sedimentary records at sites r, e Rto grid points covering the area of investigation. The locations of the rsl curves are shown in Fig. 14.5, and for site references see Table 14.2. 

Since this is an implicit equation for a, an iterative method must be used to solve for a. To evaluate u between mesh points, spatial interpolation is necessary. 

For the spatial discretization, the Finite Element Method is employed. To be more specific, the same spatial interpolation basis has been selected for the whole set of primary variables as well as for their variations, albeit this is not required. In case of linearly elastic constitutive equations, and since variations of the primary variables are independent, the following discrete system of equations is obtained ... 

The symbol ( ) denotes parameters of the spatial discretization. Moreover, matrices M, M, M, M contain the space integral of products of the selected spatial interpolation functions. It is worth noting that (Eqs. 20, 22) coincide with those presented in Simo Tarnow (1992), if we adopt the same spatial interpolation for the whole set of variables and their variations. However, in the present paper, they have been explicitly derived in a rational manner. Furthermore, (Eq. 21), which provides the basis for the consistent computation of the linear momentum of the discrete system, does not appear in the aforementioned publication. Note also that examination of the conserved currents is consistent with the weak form of Noether s Theorem as proposed in Section 5 and justifies the procedures employed by Simo Tarnow (1992). Moreover, in case of... 

In (Eqs 36-42), the symbol N(.) signifies the generalized spatial interpolation function of the variable ( ), respectively. The selection of a common interpolation basis for the variables and their variation leads to a symmetric formulation and to significant simplifications. Nevertheless, the general formulation serves as a powerful tool for tackling nontrivial problems. 

Figure 13.6. Spatial interpolation function around node k, composed of composite of local shape functions within adjoining triangular elements.

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