# create.FEM.basis: Create a FEM basis In fdaPDE: Functional Data Analysis and Partial Differential Equations (PDE); Statistical Analysis of Functional and Spatial Data, Based on Regression with PDE Regularization

 create.FEM.basis R Documentation

## Create a FEM basis

### Description

Sets up a Finite Element basis. It requires a `mesh.2D`, `mesh.2.5D` or `mesh.3D` object, as input. The basis' functions are globally continuos functions, that are polynomials once restricted to a triangle in the mesh. The current implementation includes linear finite elements (when `order = 1` in the input `mesh`) and quadratic finite elements (when `order = 2` in the input `mesh`). If saveTree flag is TRUE, it saves the tree mesh information in advance inside mesh object and can be used later on to save mesh construction time.

### Usage

```create.FEM.basis(mesh, saveTree = FALSE)
```

### Arguments

 `mesh` A `mesh.2D`, `mesh.2.5D` or `mesh.3D` object representing the domain triangulation. See create.mesh.2D, create.mesh.2.5D, create.mesh.3D. `saveTree` a flag to decide to save the tree mesh information in advance (default is FALSE)

### Value

A `FEMbasis` object. This contains the `mesh`, along with some additional quantities:

• `order`Either "1" or "2" for the 2D and 2.5D case, and "1" for the 3D case. Order of the Finite Element basis.

• `nbasis`Scalar. The number of basis.

`create.mesh.2D`, `create.mesh.2.5D`,`create.mesh.3D`

### Examples

```library(fdaPDE)
data(quasicircle2D)

## Create the 2D mesh
mesh = create.mesh.2D(nodes = rbind(quasicircle2D\$boundary_nodes,
quasicircle2D\$locations), segments = quasicircle2D\$boundary_segments)
## Plot it
plot(mesh)
## Create the basis
FEMbasis = create.FEM.basis(mesh)
data(hub2.5D)

hub2.5D.nodes = hub2.5D\$hub2.5D.nodes
hub2.5D.triangles = hub2.5D\$hub2.5D.triangles
## Create the 2.5D mesh
mesh = create.mesh.2.5D(nodes = hub2.5D.nodes, triangles = hub2.5D.triangles)
## Plot it
plot(mesh)
## Create the basis
FEMbasis = create.FEM.basis(mesh)
```

fdaPDE documentation built on Nov. 10, 2022, 5:06 p.m.