2D PDE Solution with Neumann BC: Plot Comparison

[member 428835]

Hi PF!

I'm solving a 2D PDE using NDSolveValueMesh. On one boundary I apply a Neumann BC. Attached are two plots: the top is the boundary condition and the functional value. Notice both are exactly the same.

However, the lower plot shows a directional derivative evaluated on the same boundary. Notice the plots look nothing alike.

Why is this? They seem like they should agree much more than they do. Any ideas?

 

[mmwave]

Hi there!

It's great that you're using NDSolveValueMesh to solve your 2D PDE. Neumann boundary conditions can sometimes be tricky to handle, so I can understand why you might be seeing some discrepancies in your results.

Firstly, it's important to note that a Neumann boundary condition specifies the derivative of the solution at a given boundary, rather than the solution itself. So while the top plot may show the same values for the boundary condition and the functional value, they are actually representing different quantities.

The directional derivative, on the other hand, is evaluating the change in the solution in a particular direction at the boundary. This can be affected by the shape and orientation of the boundary, as well as the behavior of the solution in that region.

Without more information about your specific problem and the boundary conditions you are using, it's difficult to pinpoint the exact reason for the discrepancies you are seeing. However, I would suggest checking the orientation and shape of your boundary, as well as the accuracy and convergence of your numerical solution.

I hope this helps! Let me know if you have any further questions or if you'd like to provide more details about your problem. Good luck with your PDE solving!