Square
The first harmonic function on a unit square with vertices \((0,0)\), \((1,0)\), \((0, 1)\) and \((1,1)\) is \[ u_\text{exact}(x, y) = \sin(\pi x)\sin(\pi y), \hspace{1em} (x,y)\in\square. \] The corresponding eigenvalue is \(2\pi^2\).
The first harmonic function on a unit square with vertices \((0,0)\), \((1,0)\), \((0, 1)\) and \((1,1)\) is \[ u_\text{exact}(x, y) = \sin(\pi x)\sin(\pi y), \hspace{1em} (x,y)\in\square. \] The corresponding eigenvalue is \(2\pi^2\).