[petsc-dev] 2D finite elements in 3D ambient space

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

[added context]

>>>> Unfortunately, something more is required for higher order accuracy,
>>>> since naively the coordinate section itself would have to be higher
>>>> order, and this would require lots of changes (the equivalent of
>>>> DMPlexComputeCellGeometry would be called once per quadrature point
>>>> instead of once per element).
>>>
>>> I have never been convinced that isoperimetric stuff produces enough benefit
>>> for its complication. Polynomials are not good approximators for the
>>> Jacobian of these transforms. NURBS are so much better.
>>
>> The value of NURBS is that (a) some coordinate transformations can be
>> represented exactly and (b) for certain problems, the rest solution can
>> be represented exactly in the ansatz space.  Quadrature error does not
>> magically vanish.
>
> My point is that trying to resolve particular geometry with polynomials is
> very slowly convergent. NURBS are much better. It depends on how
> complicated your geometry is.

I thought you were objecting to "the equivalent of
DMPlexComputeCellGeometry would be called once per quadrature point
instead of once per element".  If you were in fact agreeing with this,
and the talk of NURBS was just a tangent, then we are now on the same
page.
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