# Isoparametric Elements

**URL:** <https://community.freefem.org/t/isoparametric-elements/2730>\
**Category:** General Discussion\
**Created:** [September 28, 2023, 1:45pm UTC](https://community.freefem.org/t/isoparametric-elements/2730 "2023-09-28T13:45:20Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![yongxing](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/yongxing/32/3632_2.png) [@yongxing](https://community.freefem.org/u/yongxing)\
**Post date:** [September 28, 2023, 1:45pm UTC](https://community.freefem.org/t/isoparametric-elements/2730/1 "2023-09-28T13:45:20Z")

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Hello everyone,

You know when we compute an integration int2D( ) on a triangle, we usually transform it to a standard reference triangle to compute it.

We can easily use the shape function to do the transformation (isoparametric transformation).

My question is:  
Does FreeFem++ use the shape functions (can be second order or higher) to do the transformation?

If so, I am thinking about the boundary of a circle which can be accurately represented by the P2 element…

Thanks.  
Yongxing

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**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [September 28, 2023, 4:23pm UTC](https://community.freefem.org/t/isoparametric-elements/2730/2 "2023-09-28T16:23:45Z")

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SRory not today because I do not have this informartion in the mesh,

This is a huge change

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**Author:** ![marchywka](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@marchywka](https://community.freefem.org/u/marchywka)\
**Post date:** [September 28, 2023, 6:09pm UTC](https://community.freefem.org/t/isoparametric-elements/2730/3 "2023-09-28T18:09:55Z")

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how similar is this to conformal mapping?

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**Author:** ![yongxing](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/yongxing/32/3632_2.png) [@yongxing](https://community.freefem.org/u/yongxing)\
**Post date:** [September 30, 2023, 11:01am UTC](https://community.freefem.org/t/isoparametric-elements/2730/4 "2023-09-30T11:01:43Z")

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I tested the mesh convergence for a fluid problem using P2P1 elements and I cannot get the order of optimal convergence for the velocity: the order of L2 error for velocity is about 1.5, which is far from 3.