We consider Prandtl's boundary layer problem for incompressible laminar flow past a three dimensional yawed wedge. When the Reynolds number is large the solution of this problem has a parabolic boundary layer. We construct a direct numerical method for computing approximations to the solution of this problem using a compound piecewise-uniform mesh appropriately fitted to the parabolic boundary layer. Using this numerical method we approximate the self--similar solution of Prandtl's problem in a finite rectangle excluding the leading edge of the wedge, which is the source of an additional singularity caused by incompatibility of the problem data. By means of extensive numerical experiments, for ranges of values of the Reynolds number, wedge angle and number of mesh points, we verify that the constructed numerical method is Reynolds and angle uniform, in the sense that the computed errors for the velocity components and their derivatives in the discrete maximum norm are Reynolds and angle uniform. We use a special numerical method related to the Blasius technique to compute a semi--analytic reference solution with required accuracy for use in the error analysis.