NIST-04 (Peak)¶

This problem has an exponential peak in the interior of the domain.

Model problem¶

Equation solved: Poisson equation

(1) $-\Delta u - f = 0.$

Domain of interest: Unit Square $(0, 1)^2$ .

Boundary conditions: Dirichlet, given by exact solution.

$u(x,y) = e^{-\alpha ((x - x_{loc})^{2} + (y - y_{loc})^{2})}$

where $(x_{loc}, y_{loc})$ is the location of the peak, and $\alpha$ determines the strength of the peak.

Obtained by inserting the exact solution into the equation.

Solution for $\alpha = 1000$ , $(x_{loc}, y_{loc}) = (0.5, 0.5)$ :