Marek,

if I were you, I would first check that the assembled matrix (without 
constraints) is correct.
For a suitably small mesh you can compute the expected matrix by hand if 
necessary.
Alternatively, there is MatrixCreator::create_mass_matrix 
(https://www.dealii.org/9.0.0/doxygen/deal.II/namespaceMatrixCreator.html#a298a5ae54ecf4709eca32d9b81405274).

If that works correctly, I would try to incorporate the constraints (check 
correctness again if possible)
and use a direct (serial) solver with serial linear algebra classes.

Best,
Daniel

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