# FEM: Define a surface or spatial field by a Finite Element basis... In fdaPDE: Statistical Analysis of Functional and Spatial Data, Based on Regression with PDE Regularization

## Description

This function defines a FEM object.

## Usage

 `1` ```FEM(coeff,FEMbasis) ```

## Arguments

 `coeff` A vector or a matrix containing the coefficients for the Finite Element basis expansion. The number of rows (or the vector's length) corresponds to the number of basis in `FEMbasis`. The number of columns corresponds to the number of functions. `FEMbasis` A `FEMbasis` object defining the Finite Element basis, created by create.FEM.basis.

## Value

An `FEM` object. This contains a list with components `coeff` and `FEMbasis`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```library(fdaPDE) ## Upload the horseshoe2D data data(horseshoe2D) boundary_nodes = horseshoe2D\$boundary_nodes boundary_segments = horseshoe2D\$boundary_segments locations = horseshoe2D\$locations ## Create the 2D mesh mesh = create.mesh.2D(nodes = rbind(boundary_nodes, locations), segments = boundary_segments) ## Create the FEM basis FEMbasis = create.FEM.basis(mesh) ## Compute the coeff vector evaluating the desired function at the mesh nodes ## In this case we consider the fs.test() function introduced by Wood et al. 2008 coeff = fs.test(mesh\$nodes[,1], mesh\$nodes[,2]) ## Create the FEM object FEMfunction = FEM(coeff, FEMbasis) ## Plot it plot(FEMfunction) ```

### Example output

```Loading required package: geometry