Weak form question

Question

Hello
I want to derive the weak form of this term:

After multiplying by the test function "v" and integration by parts, could you please tell me which one is the correct weak form?

inner(nabla_grad(u), grad(v))*dx

or

inner(nabla_grad(u), nabla_grad(v))*dx

Thanks!

Answer 1

The definitions of nabla_grad and grad are given in the the FEniCS book on page 309. If you write out your expression on component form you should be able to translate your equation to the equivalent UFL notation with some basic multivariable calculus.

Sorry for not really answering your question, but you learn more by doing it yourself :-)