Small question with variational form

[bacsieboy]

I have a term in my PDE \int_{\Omega}xz\frac{\partial^2 P}{\partial x\partial z}v(\mathbf x)\,d\mathbf x where \mathbf x = [x,y,z]^T. Does this term need to be reduced? I’m not sure how to reduce this term since it contains derivative in x and z?

[Yoann]

Already answered

Variational form for multi-dimensional diffusion equation

De rien, (Are you french either by the way? ) Yes you have to reduce this term. If you suppose that P is \mathscr{C}^2 then you can choose whether x or z thanks to Cauchy-Schwarz, otherwise you should do the integration by part over x.