Mesh & pde's it can support
 

I'm looking for information relating mesh types, element order, element shape against various pde types.

Essentially, what level of physical phenomena can a particular mesh arrangement support - without requiring local mesh optimisation - ie. a uniform mesh.

Links & references would be gratefully appreciated. Thanks so much.

desA

Re: Mesh & pde's it can support
 

No takers? :(

I'll kick off with a simple cos() function requiring at least a P6 (28 node triangle) to capture the first 4 terms of the cos() Taylor expansion & to capture a full cycle.

To get around this obvious limitation, using lower order finite elements, we can cut the cos() form into pieces. The more we cut, the smaller the element size required for lower-order element interpolation functions. This ends up in an ever-increasing demand for elements, the lower the level of element used.

Has anyone worked with alternative element interpolation functions eg. exp, cos, sin, cosh etc?

desA