How much new programming work would it be to evaluate Expressions on all points of integration grid

Question

Dear All

Further to my question yesterday.
How much work coding is needed to allow
for the more accurate evaluation of matrix elements of Expressions by
evaluating these expressions on the integration grid instead of interpolatiing them?

regards

Moritz

Comments

No work need to be done as it is already supported. Use Quadrature elements as Garth already pointed out for you in your previous question.

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Dear Johan

Your are not correct.
Using a function space of higher order is not the same as
evaluating the potential on directly on the integration grid!
I tried to use 10th order polynomials and my job ran out of memory on a 8Gb laptop.

regards

Moritz

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I did not say use higher order element. I said use Quadrature elements, as did Garth in the previous question.

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Dear Johan
Please note.
Using quadrature element does not help, since the
Expressions are still interpolated on the nodal points
instead of on the integation grid!

regards

Moritz

Answer 1

I believe what you're looking for is Gauss-Lobatto quadrature. It is a quadrature rule where the integration points coincide with the mesh nodes.

I'm a fenics novice, but I am very familiar with the method. It seems to be in fenics already. I found it here:

http://fenicsproject.org/documentation/dolfin/1.0.0/cpp/programmers-reference/quadrature/LobattoQuadrature.html