csrc-sdsu / csrc-sdsu/mole

Add a Mimetic Operator Vs Finite Difference tutorial with a step-by-step explanations and comparisons

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Description

**Is your feature request related to a problem? Please describe.**
We need a simple step-by-step tutorial that showcases the mimetic properties as opposed to other familiar discretization methods that people with an entry-level knowledge (e.g., students) can grasp, such as Finite Differences (FD). Something that shows when the mimetic discretization is better than the other.

**Describe the solution you'd like**

Can we find a discerning test case that showcases that this method is really superior? For instance could we provide an example in which being just high-order FD, but not mimetic, makes the difference? And then compare the same example using the MOLE operators?

After this, we could add an efficiency-focused benchmark to report on the MOLE operators efficiency. It would be useful to have benchmarks in this regard for new users/application developers that approach the library.

**Describe alternatives you've considered**
An alternative could be comparing a MOLE example with a high-order FEM/SEM example from another package, e.g., libCEED.

**Additional context**
Some of the suggestions came up from the ICorps interviewees.

cc: @jbrzensk , I think you gave a sort of similar tutorial at the beginning of the academic year for the master students working in the project. Can we re-use part of that and make it a tutorial in our documentation?

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