fdaPDE (version 0.1-3)

create.FEM.basis: Create a FEM basis

Description

Sets up a Finite Element basis. It requires a triangular mesh, a MESH2D object, as input. The basis' functions are globally continuos surfaces, that are polynomials once restricted to a triangle in the mesh. Linear if (order = 1) in the input mesh and quadratic if (order = 2) in the input mesh Finite Element are currently implemented.

Usage

create.FEM.basis(mesh)

Arguments

mesh

A MESH2D object representing the domain triangulation. See create.MESH.2D.

Value

• A FEMbasis object. This contains the mesh, along with some additional quantities:
• order
  Either "1" or "2". Order of the Finite Element basis.
• nbasis
  Scalar. The number of basis.
• detJ
  The determinant of the transformation from the nodes of the reference triangle to the nodes of the i-th triangle; this coincides with the double of the area of the i-th triangle.
• transf
  A three-dimensional array such that transf[i,,] is the 2-by-2 matrix that transforms the nodes of the reference triangle to the nodes of the i-th triangle.
• metric
  A three-dimensional array such that metric[i,,] is the 2-by-2 matrix transf[i,,]^{-1}*transf[i,,]^{-T}. This matrix is used for the computation of the integrals over the elements of the mesh.

See Also

create.MESH.2D

Examples

## Creates a simple triangulated domain with a concavity; this is a MESH2D object  
mesh<-create.MESH.2D(nodes=rbind(c(0, 0), c(0, 1), c(0.5, 0.5), c(1, 1), c(1, 0)),
segments=rbind(c(1, 2), c(2, 3), c(3, 4), c(4, 5), c(5, 1)), order=1)
## Plot it
plot(mesh)                   
## Creates the basis
FEMbasis = create.FEM.basis(mesh)