# Convergence In the Poiseuille Equation

Consider a mesh as follows (Which is a unit square):

I solved the Poiseuille equation by using the exact same code as mentioned in the tutorial

Then, I chose 100 points spread uniformly across this unit square (Need not to be the grid points). Let’s call them as X_{grid}.

After that I evaluated the velocity values in this X_{grid}. Let’s denote these set evaluated velocity values as V^1_{grid}.

Next, I reduced the mesh size, Solved the Poiseuille equation and again evaluated the velocity values in the X_{grid} points. Call it V^2_{grid}

I continued to do reduce the mesh sizes and evaluated the velocity values in the same X_{grid} points. That is: V^3_{grid}, V^4_{grid}, V^5_{grid}

So, technically as I’m refining the mesh, the velocity values should be closer to the exact answer in the latter solutions.

However, when I evaluate the exact solution in the X_{grid}, call it as V_E and the difference was taken, That is:
||V^1_{grid}-V_E||, ||V^2_{grid}-V_E||, ||V^3_{grid}-V_E||, ||V^4_{grid}-V_E||, ||V^5_{grid}-V_E||, ||V^6_{grid}-V_E||, ||V^7_{grid}-V_E||, ||V^8_{grid}-V_E|| 