# Is the KMV Element Available in FreeFEM?
**URL:** https://community.freefem.org/t/is-the-kmv-element-available-in-freefem/4142
**Category:** Feature Request
**Created:** [November 26, 2025, 10:12am UTC](https://community.freefem.org/t/is-the-kmv-element-available-in-freefem/4142 "2025-11-26T10:12:46Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@thingway](https://community.freefem.org/u/thingway)
#### Post date: [November 26, 2025, 10:12am UTC](https://community.freefem.org/t/is-the-kmv-element-available-in-freefem/4142/1 "2025-11-26T10:12:46Z")
After reading the FreeFEM documentation, I could not find any function or element corresponding to the KMV (Kong-Mulder-Veldhuizen) element, as described on DefElement: [https://defelement.org/elements/kong-mulder-veldhuizen.html](https://defelement.org/elements/kong-mulder-veldhuizen.html). This element is particularly useful for implementing mass-lumped triangular or tetrahedral finite elements. Is there currently a method to use it in FreeFEM, or is this planned for a future update?
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### Author:  [@fb77](https://community.freefem.org/u/fb77)
#### Post date: [November 26, 2025, 11:35am UTC](https://community.freefem.org/t/is-the-kmv-element-available-in-freefem/4142/2 "2025-11-26T11:35:30Z")
In the link you mention, the description corresponds to (at least if continuity is required, there is no mention on this)
degree 1 : P1
degree 2 : P2b (P2+bubble)
The only “difference” is that the normalisation (factors 6 or 40…) is unusual.
This could be managed with a diagonal matrix multiplication.
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### Author:  [@thingway](https://community.freefem.org/u/thingway)
#### Post date: [November 26, 2025, 12:09pm UTC](https://community.freefem.org/t/is-the-kmv-element-available-in-freefem/4142/3 "2025-11-26T12:09:12Z")
Thank you for your kind reply. I agree the KMV element and quadrature are trivial for degree=1. For degree=2, I will review the information you shared.
> [@fb77](#):
>
> degree 2 : P2b (P2+bubble)
I should clarify a key point I omitted earlier: implementing mass-lumped triangular elements requires both special basis functions and a matching quadrature rule, as detailed in this article: [Higher-order triangular and tetrahedral finite elements with mass lumping for solving the wave equation | Journal of Engineering Mathematics | Springer Nature Link](https://link.springer.com/article/10.1023/A:1004420829610) . Thus, given that a special quadrature rule is also required for degree \>= 2, what is the recommended approach to implement this custom quadrature rule? Thank you again.
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### Author:  [@fb77](https://community.freefem.org/u/fb77)
#### Post date: [November 26, 2025, 12:34pm UTC](https://community.freefem.org/t/is-the-kmv-element-available-in-freefem/4142/4 "2025-11-26T12:34:20Z")
Different quadrature rules are defined in FreeFem for triangles.
They are described in
> **[FreeFEM-documentation.pdf](https://doc.freefem.org/pdf/FreeFEM-documentation.pdf)**
>
> 33.85 MB
p.226
On this page the keywords are slightly erased. Their full names can be seen at
> **[Quadrature formulae](https://doc.freefem.org/references/quadrature-formulae.html#qf2pt)**
I think it is not possible for the user to define new quadrature rules.
The P2b element is described in the pdf above, p.197
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### Author:  [@thingway](https://community.freefem.org/u/thingway)
#### Post date: [November 26, 2025, 12:58pm UTC](https://community.freefem.org/t/is-the-kmv-element-available-in-freefem/4142/5 "2025-11-26T12:58:00Z")
Thank you for your reply. Based on our discussion, it seems that implementing mass-lumped triangular or tetrahedral elements in FreeFEM is currently non-trivial. I will continue learning this software and look forward to future developments. It was a very helpful discussion. Thank you again.😀