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0mar / dealiiscale

Finite element simulation of a two-scale problem implemented in deal.II
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Integration of solution approximations #7

Closed 0mar closed 5 years ago

0mar commented 5 years ago

Find out how I can reliably integrate a solution approximation (DoF length vector) in deal.II. The way I have it now seems to work but is untested, see 8a5e09f

0mar commented 5 years ago

Closed with bdfa9cf. Using third order quadrature integration, we obtain the following errors.

cycle cells   dofs     L2        int      normal
    0   5120   5185 1.509e-03 -3.936e-04 8.271e-02
    1  20480  20609 3.775e-04 -9.859e-05 3.951e-02
    2  81920  82177 9.437e-05 -2.466e-05 1.929e-02
    3 327680 328193 2.359e-05 -6.166e-06 9.531e-03

where int represents the error made in the bulk integral and normal represents the error made with the flux integral over the boundary. We see linear convergence in the flux integral errors, due to the evaluation of the solution gradient, and quadratic convergence in the bulk errors, so that should behave as expected.