I am trying to solve Laplace's equation in 2 dimensions with potencial boundary conditions at the edges of an external square and an internal circle. Everything seems to work fine until the point where I try to obtain a DensityPlot to visualize the the obtained potential at all points. When I execute the density plot line, I am returned with a diagram that displays the solution of the equation for only a fraction of the region where I solved the equation. How can I fix this ? The code is as follows:
α =
RegionDifference[Rectangle[{-50, -50}, {50, 50}], Disk[{0, 0}, 5]]
sol = NDSolveValue[{D[u[x, y], x, x] + D[u[x, y], y, y] == 0,
DirichletCondition[u[x, y] == 100, x^2 + y^2 == 25],
u[x, -50] == u[x, 50] == u[-50, y] == u[50, y] == 0},
u, {x, y} ∈ α]
DensityPlot[sol[x, y], {x, y} ∈ α, Mesh -> None,
ColorFunction -> "Rainbow", PlotRange -> All,
PlotLegends -> Automatic]