rSPDE.fem2d: Finite element calculations for problems in 2D

In rSPDE: Rational Approximations of Fractional Stochastic Partial Differential Equations

Finite element calculations for problems in 2D

Description

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).

Author(s)

David Bolin [e-mail]

See Also

rSPDE.fem1d()

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)

rSPDE documentation built on Jan. 26, 2026, 9:06 a.m.