FEM: Define a surface or spatial field by a Finite Element basis...

In fdaPDE: Physics-Informed Spatial and Functional Data Analysis

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)
## Upload the horseshoe2D data
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 March 7, 2023, 5:28 p.m.