# NIST-08 (Oscillatory)

This problem is inspired by the wave function that satisfies a Shrodinger equation model of two
interacting atoms. It is highly oscillatory near the origin, with the wavelength decreasing closer
to the origin.

## Model problem

Equation solved: Hemholtz equation

where . The number of oscillations, , is determined by the parameter

Domain of interest: Unit Square .

Boundary conditions: Dirichlet, given by exact solution.

## Right-hand side

Obtained by inserting the exact solution into the equation.

## Sample solution

Solution for :

## Comparison of h-FEM (p=1), h-FEM (p=2) and hp-FEM with anisotropic refinements

Final mesh (h-FEM, p=1, anisotropic refinements):

Final mesh (h-FEM, p=2, anisotropic refinements):

Final mesh (hp-FEM, h-anisotropic refinements):

DOF convergence graphs:

CPU convergence graphs:

## hp-FEM with iso, h-aniso and hp-aniso refinements

Final mesh (hp-FEM, isotropic refinements):

Final mesh (hp-FEM, h-anisotropic refinements):

Final mesh (hp-FEM, hp-anisotropic refinements):

DOF convergence graphs:

CPU convergence graphs: