Massively lower some IDA solver tolerances.

[drwells]

ida_02 presently fails with a numdiff difference of about 1e-6: this makes sense since that's the provided solver tolerance. We can get consistent results by making it a few orders of magnitude lower.

[drwells]

Part of #13703.

[kronbichler]

On the serial CI, the first test still seems to fail:

sundials/ida_01.debug: DIFF failed. ------ First 20 lines of numdiff output:
----------------
##2       #:2   <== 0.198666
##2       #:2   ==> 0.198669
@ Absolute error = 3.0000000000e-6, Relative error = 1.5100721815e-5
##2       #:3   <== 0.98005
##2       #:3   ==> 0.980067
@ Absolute error = 1.7000000000e-5, Relative error = 1.7346053773e-5
##2       #:4   <== 0.980056
##2       #:4   ==> 0.980067
@ Absolute error = 1.1000000000e-5, Relative error = 1.1223848433e-5
##2       #:5   <== -0.198643
##2       #:5   ==> -0.198669
@ Absolute error = 2.6000000000e-5, Relative error = 1.3088807559e-4
----------------
##3       #:2   <== 0.389414
##3       #:2   ==> 0.389418
@ Absolute error = 4.0000000000e-6, Relative error = 1.0271844361e-5
##3       #:3   <== 0.921051
##3       #:3   ==> 0.921061
@ Absolute error = 1.0000000000e-5, Relative error = 1.0857162090e-5

[marcfehling]

ida_02 presently fails with a numdiff difference of about 1e-6: this makes sense since that's the provided solver tolerance. We can get consistent results by making it a few orders of magnitude lower.

You meant ida_01, right?

This change shouldn't increase runtime significantly, so to me this is fine.

[drwells]

Both, actually, and they both use the same prm file.

[bangerth]

This is ok with me. Do I understand @kronbichler 's comment as an objection?