# Small question with variational form

**URL:** <https://fenicsproject.discourse.group/t/small-question-with-variational-form/3616>\
**Category:** variational formulation\
**Created:** [June 23, 2020, 2:42pm UTC](https://fenicsproject.discourse.group/t/small-question-with-variational-form/3616 "2020-06-23T14:42:11Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![bacsieboy](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/bacsieboy/32/1447_2.png) [@bacsieboy](https://fenicsproject.discourse.group/u/bacsieboy)\
**Post date:** [June 23, 2020, 2:42pm UTC](https://fenicsproject.discourse.group/t/small-question-with-variational-form/3616/1 "2020-06-23T14:42:11Z")

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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?

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**Author:** ![Yoann](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@Yoann](https://fenicsproject.discourse.group/u/Yoann)\
**Post date:** [June 23, 2020, 4:04pm UTC](https://fenicsproject.discourse.group/t/small-question-with-variational-form/3616/2 "2020-06-23T16:04:48Z")

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Already answered 😉

> [@Variational form for multi-dimensional diffusion equation](https://fenicsproject.discourse.group/t/variational-form-for-multi-dimensional-diffusion-equation/3606/7):
>
> 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.