Finite element calculations for problems in 2D

This function computes mass and stiffness matrices for a mesh in 2D, assuming Neumann boundary conditions.

Usage

rSPDE.fem2d(FV, P)

Arguments

FV

Matrix where each row defines a triangle

P

Locations of the nodes in the mesh.

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

The mass lumped matrix with diagonal elements \((\phi_i, 1)\).

Hxx

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

Hyy

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

Hxy

Matrix with elements \((\partial_x \phi_i, \partial_y \phi_j)\).

Hyx

Matrix with elements \((\partial_y \phi_i, \partial_x \phi_j)\).

Bx

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

By

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

See also

rSPDE.fem1d()

Author

David Bolin davidbolin@gmail.com

Examples

P <- rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1))
FV <- rbind(c(1, 2, 3), c(2, 3, 4))
fem <- rSPDE.fem2d(FV, P)