NDSolve[{-Laplacian[u[x, y], {x, y}] == 0, DirichletCondition[u[x, y] == Boole[y >= 0], True]}, u, {x,y} [Element] Disk[]];Plot3D[Evaluate[u[x, y] /. %], {x, y} [Element] Disk[],PlotPoints -> 100, PerformanceGoal -> "Quality"]