# Excluding gradients in regions of a mesh

2 months 1 week ago #2489
Hi,

On a previous post to the forum, you kindly told us about the possibility of removing the gradients from a H(curl) discretisation when solving magnetostatic problems or eddy current problems (ie removing them from free space in this case). I’ve been seeing a few strange results when looking at p-convergence of eddy current problems at high p and to test it I have written a simple script.

The script solves a magnetostatic problem

curl curl Theta =0 in Omega,
div Theta =0 in Omega
nx Theta = n x f on partial Omega

with f being chosen such that it satisfies the equations in Omega. The divergence condition is circumvented through regularisation. I have tried removing the gradients in part or all of the domain, but when I do this the H(curl) error appears to stagnate under p-refinement - there is little change between p=2 and p=3 and after p=3 no further reduction in error. However, if the gradients are included in the H(curl) discretisation, the error continues to go down. I’ve tried it with and without static condensation and the issue appears to be the same.

Could there perhaps be bug with removing the gradients with high p, or am I just using this incorrectly?

The results below illustrate the convergence behaviour I’m seeing. They quote the order, ndof and the relative H(curl) error.

0 4383 0.0011789945467936594
1 8766 0.0009373029532722708
2 35277 3.4731510020002566e-05
3 91220 3.8663715608261767e-07
4 187605 1.0743507025059146e-08
5 335442 3.370498335025573e-11

0 4383 0.001178994546793698
1 8766 0.0009373029532667969
2 35277 3.4731510019407475e-05
3 91220 3.866381307337492e-07
4 187605 1.0747153600760681e-08

0 4383 0.0011789945467942453
1 5253 0.001329978591542595
2 21968 7.933377743385801e-05
3 58593 5.919570304667666e-05
4 122899 5.978401345138389e-05
5 222657 5.979437345636938e-05

0 4383 0.0011789945467944511
1 5253 0.0013299785915435224
2 21968 7.933377743386192e-05
3 58593 5.9195703046669775e-05
4 122899 5.9784013540558305e-05

0 4383 0.0011789945467940678
1 4383 0.0011789945467943668
2 19135 0.0003520548444002678
3 52273 0.0003289227799904819
4 111137 0.00022283611822004694

0 4383 0.0011789945467937117
1 4383 0.0011789945467930313
2 19135 0.0003520548444002607
3 52273 0.0003289227799904705
4 111137 0.0002228361182200561
5 203067 0.0002305775449743086

Thanks very much for your help

Ben.