Output relative errors

ASPECT
1

Hi all,

I am wondering for benchmark problems, is there a straight forward way to output relative errors? I understand dealii doesn’t have the method for that in the VectorTools namespace, so I am quite curious if there is any template to follow.

Thanks,
Regards,
Ray

2

The function in VectorTools exists alright.

I think you should take a look at how the error is computed for some of the
other benchmarks in the benchmarks/ folders.

Best
W.

3

Hi Wolfgang,

Thanks, but are you referring to VectorTools::L1_norm/L2_norm? Cause I thought those are just absolute error norm instead of relative ones with respect to exact solutions.

Regards,
Ray

4

Right. They give you the enumerator of the ratio. You just need the
denominator in that case, which I would choose as the maximum of the solution.
Or how exactly do you define “relative error”?

Best
W.

5

For the denominator, I am thinking of the exact solution at each cell. (i.e. || u - u_e || / || u_e || )

Ray

6

For the denominator, I am thinking of the exact solution at each cell. (i.e.

u - u_e || / || u_e || )

The usual way to do this would actually be to divide by

u_e ||
which is something that you can easily get by writing it as
0 - u_e ||
which in turn you can get by calling VectorTools::integrate_difference() where
instead of the exact solution you pass Functions::ZeroFunction instead.

Best
W.

7

Somehow I produced an error that “expected primary expression before ‘)’ token”

My code for VectorTools::Integrate_difference is like the following,

 VectorTools::integrate_difference (this->get_mapping(),
				 this->get_dof_handler(),
				 this->get_solution(),
				 Functions::ZeroFunction<dim>(),
				 cellwise_errors_uhl2,
				 quadrature_formula,
				 VectorTools::L2_norm,
				 &comp_uh);

I was trying to follow the syntax in the dealii tutorial step-64, but I am wondering if I have to fill in some additional expressions.

Thanks in advance,
Ray

8

I was trying to follow the syntax in the dealii tutorial step-64, but I am
wondering if I have to fill in some additional expressions.

You’ll have to show us more of the code and what line the error message
corresponds. It’s possible that &comp_uh causes the problem that you’re
seeing, but I don’t know what comp_uh actually is.

Once it compiles, you will get a run-time error because
Functions::ZeroFunction()
creates a scalar function object, but you need one that has as many vector
components as the solution vector has components. That number should go into
the parentheses.

Best
W.

9

Hi Wolfgang,

Sorry for not making this clear, but I believe I have figured out the problem.

First for “comp_uh”, this is just a variable for the “ComponentSelectFunction” in this case, but it may not be necessary as normal “comp_u” (or comp_p for pressure) also works.

Second, indeed I need to fill the number of components in the parentheses, but it still produces the error of “error: reference to ‘ZeroFunction’ is ambiguous”, so instead of using Functions:ZeroFunction(), I just called ZeroFunction(), which somehow resolved the issue.

Again much appreciated of your help, thanks a lot.
Ray