On 6/24/21 8:50 AM, Alex Cumberworth wrote:
I am working with a mesh generated from subdivided_cylinder, and am wondering
whether the area and volume should be assumed to match that of a true
cylinder, or if it only converges to that when many refinements are made. I
would like to calculate the total energy of the system by integrating over the
whole volume, as well as calculate shear forces by integrating over faces on
the surface.
That depends on whether you use a mapping argument in the integration or not.
If not, then you are implicitly using a Q1 mapping for all cells, which is not
going to provide a particularly accuracte approximation of volume and area. On
the other hand, if you use a MappingQ(4) or even better MappingManifold, and
if you use a sufficiently high order quadrature formula, then you should be
very close to the exact volume/area already on a fairly coarse mesh.
In no case will things be exact: Even with MappingManifold, you are still
computing integrals that you approximate via quadrature.
I have no opinion on what might be wrong with your beam example :-)
Cheers
W.
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Wolfgang Bangerth email: [email protected]
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