Finite element calculations for problems on R

This function computes mass and stiffness matrices for a FEM approximation on R, assuming Neumann boundary conditions. These matrices are needed when discretizing the operators in rational approximations.

Usage

rSPDE.fem1d(x)

Arguments

x

Locations of the nodes in the FEM approximation.

Value

The function returns a list with the following elements

G

The stiffness matrix with elements \((\nabla \phi_i, \nabla \phi_j)\).

C

The mass matrix with elements \((\phi_i, \phi_j)\).

Cd

Mass lumped mass matrix.

B

Matrix with elements \((\nabla \phi_i, \phi_j)\).

See also

rSPDE.A1d()

Author

David Bolin davidbolin@gmail.com

Examples

# create mass and stiffness matrices for a FEM discretization on [0,1]
x <- seq(from = 0, to = 1, length.out = 101)
fem <- rSPDE.fem1d(x)