Dear all, if we have a Function u and we want to calculate \frac{\partial{u}}{\partial{x}}, we use u.dx(0). Now I need to calculate the derivative of Function u with respect to a direction, I showed this direction in the following figure: [Screenshot from 2024-06-23 13-18-37] Does anyone know how…

The small snippet looks fine to me. The best thing to do is to test it with a known u and v and see if you get what you expected.

I can interpret from your figure that you want to compute the gradient in the normal direction at a facet. What you would then do is n = ufl.FacetNormal(mesh) dudn = ufl.dot(ufl.grad(u), n) This can then in turn be used in variational formulations with the ds or dS integral measure. If you want …

Thank you for your kind help, Dokken. I am using the legacy dolfin on ubuntu. I think my version is the latest legacy dolfin since I installed it last year (I don’t know how to check the version). I use fenics to study the adhesive interface in solid mechanics. My whole code is long. To illustrate …

See: How ufl.nabla_grad works? - #2 by dokken

Yes. I have seen this before. In my opinion, nabla_grad should be used here. Could you please tell me if the other parts of my code is correct? :slightly_smiling_face:

Ok. Thank you very much for your kind help. :slightly_smiling_face:

Dear Dokken, I tested my code shown above. The result is correct. But it seems that when I included dwdn=dot(nabla_grad(w), n) and dvdn=dot(nabla_grad(v), n) into the variational form, just like the variational form I showed above: variational_form = ( ...... + dot(dwdn, dvdn) )*dx, the computation…

I would check what the estimated polynomial degree of the term is using ufl: [image] How many integration points are included in the tetrahedral grid? mesh The number of quadrature (gauss) points is estimated by ufl when you specify your variational form. See for instance…

Calculate the derivative of a Function with respect to a direction

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dokken June 24, 2024, 10:00am 9

I would check what the estimated polynomial degree of the term is using ufl:

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Calculate the derivative of a Function with respect to a direction

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