# FiniteElementDegree¶

Type: | Vector<int>, or section |
---|---|

Range: | [v_1, …, v_3] |

Default: | -/- |

Appearance: | optional |

Sets the polynomial order of the finite element *initial* discretization. Two strategies are supported:

User-defined global setting

Defining a fixed single value, e.g.,

```
FiniteElementDegree = 3
```

results in a global choice of the finite element order for all patches of the mesh. With a vector value, e.g.

```
FiniteElementDegree = [2 2 4]
```

different polynomial orders are used for the three Cartesian space directions. This latter choice can be used when the mesh elements are aligned along at least one coordinate axis (e.g., in meshes created by extruding a 2D triangular mesh in the third dimension / prismatoidal meshes, different polynomial orders can be chosen in the third dimension and in the lateral dimensions).

Self-adaptive control

When not defining a global, fixed finite element degree, `JCMsolve`

uses a self-adaptive strategy for locally setting the finite element degree.
In a nutshell this is done as follows:

The finite element technology is based on an approximation of the solution field by means of ansatz functions which have local support and which are polynomials on each patch of the (refined) mesh.
The higher the finite element degree the better is the approximation.
Hence, increasing the finite element degree will yield better solution on the same mesh.
This is called -refinement ( stands for polynomial).
`JCMsolve`

automatically adapts the finite element order, so that an accuracy of Precision is reached in any region where the field is sufficiently smooth.
In terms as defined in the section on Accuracy the automatic -adaption controls the smooth part of the error.

The -adaption strategy supplements the mesh refinement strategy, where the mesh is adaptively refined in order to increase the approximation quality, c.f., Refinement. The mesh refinement strategy is called -refinement.

Solution fields with, e.g., a singularity-like behavior near material corners, require -refinement, whereas smooth fields are better approximated with higher order finite elements. Therefore the best choice of the finite element degree depends on the actual simulation project and one is advised to perform convergence tests in order to fix the optimal finite element degree for the specific problem class.