Hello,
In a linear elasticity problem, where on the inner boundary of a spherical shell, dynamic pressure is applied, I have tested the results with various mesh resolutions. The best results (compared to exact solution) are derived with a mesh that its resolution is a function of radius and with higher radius gets coarser. First, how can I know the best way to build mesh on any geometry? Second, I’ve noticed that in this specific problem, when I use second order CG elements, the results on the inner boundary are very good, while that of the outer boundary differs a lot from the exact solution. Can anybody offer any suggestion on this? What could be the problem that the second order elements behave like this?
Thanks in advance.
Without a variational formulation it is really hard to give any guidance. Usually you will see improved convergence rates when using a higher order basis function (if the geometry is sufficiently resolved).
Building good meshes is a research question when you say arbitrary geometry.
There are many meshing tools out there that lets you customize anything from mesh resolution, to boundary layers and the curving (order) of each element in the mesh geometry:
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