Are there capabilities for adaptive quadrature?

Question

I'm working on computing discretization errors for boundary layer solutions, which usually require adaptive quadrature to accurately resolve the error. I'm currently refining the mesh near the boundary layer, interpolating the coarse solution over, and computing the error on the refined mesh. Is there a more efficient way to do this?

Thanks!

Comments

To be clearer, the diffusivity (and hence width of the boundary layer) can be extremely small (near 1e-6), and I'm interested in showing that our error estimator is independent of diffusivity. This requires computing the pointwise error in a boundary layer solution accurately.

Answer 1

The FFC generated code will integrate polynomial terms exactly, so increasing the quadrature degree will make no difference.

If you want to compute the error relative to an exact solution, you can use a high-order element to interpolate the exact solution.