Boundary Condition Example

[12jordans]

Hello,

I was interested in adding boundary conditions to a tutorial example from issue #231. I also wanted to convert the example into C++. Please let me know if this is wanted and also if there is any other information I should know.

[valeriabarra]

@jbrzensk if you have any advice, please let us know!

[valeriabarra]

This relates to Issue #231

[jbrzensk]

Sounds good. I recommend something with Neumann boundary conditions. Those are very hard to hand-code a boundary operator with >1 order accuracy. The example should show some error convergence, and let the user change the order of accuracy of the mimetic operators to get a higher order approximation. Assume the user will not change the finite difference example.

[12jordans]

@jbrzensk Do you want the Neumann boundary conditions added to the existing tutorial on the two way wave equation or is this supposed to be a new tutorial?

[jbrzensk]

Make it a separate file in the same tutorial directory. Similar naming. "comparison_two_way_with_neumann.m" or something.

[12jordans]

@jbrzensk I noticed that the existing tutorial shows that the mimetic difference error slope is greater than the finite difference error slope. Is this expected behavior? I tried comparing the errors with the energy norm on my BC tutorial, but I am still getting the same results. Any guidance on this issue would be very helpful.

[jbrzensk]

Thanks, @12jordans, good catch. The tutorial needs to be updated. I will make an issue.

Try the version from the MATH693B branch..

Notably, it changes how the error is calculated and the function for the initial conditions.

It also lets you play with the wave speed, dt, and grid cells more easily so you can see the changes.

[12jordans]

Thank you! I will use that version and update my code.

[jbrzensk]

@12jordans The tutorial has been updated. If you git pull, you should get an updated tutorial on the main branch that shows the plots above.