# When the data is given but not the analytical solution, how to find out L2H1 error for heat equation

**URL:** <https://community.freefem.org/t/when-the-data-is-given-but-not-the-analytical-solution-how-to-find-out-l2h1-error-for-heat-equation/3397>\
**Category:** General Discussion\
**Created:** [July 15, 2024, 1:30pm UTC](https://community.freefem.org/t/when-the-data-is-given-but-not-the-analytical-solution-how-to-find-out-l2h1-error-for-heat-equation/3397 "2024-07-15T13:30:14Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Shrvs](https://avatars.discourse-cdn.com/v4/letter/s/7ba0ec/32.png) [@Shrvs](https://community.freefem.org/u/Shrvs)\
**Post date:** [July 15, 2024, 1:30pm UTC](https://community.freefem.org/t/when-the-data-is-given-but-not-the-analytical-solution-how-to-find-out-l2h1-error-for-heat-equation/3397/1 "2024-07-15T13:30:14Z")

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To be precise after finding the reference solution with the given data on finer mesh (tau=1/2^9, h=1/80)and approximate solution on coarser mesh(spatial and time points are less(tau=1/2^4, h=1/10) in comparison with the reference solution obtained on refined mesh), how to proceed further to obtain L2H1 error for the given heat equation. Could you please help me in this regard.  
Thanks.