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

 FEM R Documentation

Define a surface or spatial field by a Finite Element basis expansion

Description

This function defines a FEM object.

Usage

```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

```library(fdaPDE)
data(horseshoe2D)

## Create the 2D mesh
mesh = create.mesh.2D(nodes = rbind(horseshoe2D\$boundary_nodes, horseshoe2D\$locations),
segments = horseshoe2D\$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)
```

fdaPDE documentation built on Nov. 10, 2022, 5:06 p.m.