"Garth N. Wells" <[email protected]> writes: >> Ignoring non-zero degree of f >> (which seems to me you do suggest for a and L) means that you're >> underintegrating any of those three forms. > > Yes, as is what happens in many FE codes where the quadrature scheme is > determined by the polynomial order of the product test and trial > functions.
Yup, underintegration is a fact of life and fairly benign most of the time. I would like to mention two cases that I haven't seen mentioned yet, and for which "thinking in polynomials" is harmful: 1. non-smooth function, such as when there is some critical microscale phenomenon like phase change. 2. non-deterministic function, such as when the value is the result of a Monte Carlo microscale simulation (statistics only homogenize to a tolerance which might be less than FE discretization error) or stochastic noise term. Unlike aliasing in Navier-Stokes, when quadrature error causes problems in these cases, raising the quadrature degree usually makes the problem worse rather than better.
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