# NIST-10 (Interior Line Singularity)

This example is an extension of Boundary Line Singularity (NIST-07) with an anisotropic solution to allow
for a sloped line so that the singularity does not necessarily coincide with element edges.

## Model problem

Equation solved: Poisson equation

(1)

Domain of interest: .

Boundary conditions: Dirichlet, given by exact solution.

## Exact solution

where and are real constants.

## Right-hand side

Obtained by inserting the exact solution into the equation.

## Sample solution

Solution for and :

## 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: