[dune-pdelab] parallel L2-error norms and parallel volume integrals

[Michael Wenske]

Dear List,

i'm having problems verifying my numerics in a parallel DUNE-PDELab setting.

Im on Dune 2.6, I use a Yasp grid and solve Darcy-like equations.

I constructed an analytical solution, which I can interpolate and write
to .vtk files
together with the numerical solution.
I can compare the numerical solution and the analytic solution with the
tools
Paraview provides (Calculator-filter and Integrate Variables etc. ). And
so far things look wonderful,
but this way I rely on the correctness of the Paraview implementation.
And I have to click a lot.

Now I want to do the same thing in the code in a more automated fashion.
Is there PDELab functionality to -globally- compare and analyze two
solutions?

I tried:

    double get_error_norm(const RHSType& numeric_sol, const RHSType&
analytic_sol){
                auto difference = numeric_sol-analytic_sol;        //Fail
                ISTLHelperType parHelper(*gfs_p);
                Dune::PDELab::OverlappingScalarProduct<GFS,RHSType>
ovlp_scalar_prod(*gfs_p,parHelper);
                double norm =ovlp_scalar_prod.norm(difference);
                return norm;
    }

where RHSType is :"Dune::PDELab::Backend::Vector<GFS,RangeFieldType>"

but it seems that there are no parallel operators implemented to do *=,
+, - on these Vector types.
Technically the above approach is not correct, as not every coefficient
should be weighted in the same way.
Coefficients which lie on the Border of the domain (Q1, quadrilateral)
should be counted half/quarter.

I might force my Local operator to do such operations, since the Methods
are provided with the necessary
Information upon assembly, but it seems wrong to me to mix the numerical
solution steps with the analysis-related
code.

If I would set up something like a AnalyserLocalOperator, how would I
traverse this correctly? Currently I pass
The local operators as template types to the solvers, but in this case
there is nothing to solve.
The whole Abstraction of the Local Operator is pointed towards
assembling a Matrix( for a Solver), so If I just want
to analyze my solution w.r.t volume, histogram, L2 error against
analytic sol etc. is this still the correct approach?

This might be trivial for the ol' folks but I can't seem to figure out a
clean way to do this.

thanks in advance,

Michael Wenske