# School - Fundamentals and practice of finite elements

## Travaux Pratiques (TP)

We propose 4 series of practical exercises (TP for "Travaux Pratiques") using XLiFE++.

### Helmholtz problem in a wave guide (TP1)

The goal of this TP is to experiment several strategies to compute the solution of a wave propagation problem in a closed wave guide. The 2D acoustic Helmholtz problem is considered with an obstacle inside the wave guide.

This TP is proposed by N. Kielbasiewicz and E. Lunéville.

### Eigenvalue computations (TP2)

The goal of this TP is to see how to compute the eigenvalues and some properties of these computations. The operator is the Dirichlet Laplacian on a square $\pi \times \pi$. The exact eigenvalues are all sums of squares of two integers $m^2+n^2$, with $m>0$, $n>0$.

Exercise 1 consists in performing the "p-version" (i.e. increasing the interpolation degree) to compare different interpolations (uniform and Gauss-Lobatto). Exercise 2 consists in performing the "h-version" on nested trianglular meshes with different types of finite elements (Lagrange and Crouzeix-Raviart).

Solutions to exercises 1 and 2

This TP is proposed by Zoïs Moitier as an illustration of the talks by Monique Dauge.