The GLL method cannot perform exact numerical integration for DGSEM ？

[teddyz1999]

When using GLL nodes, employing the same nodes for both interpolation and quadrature is known as collocation. For example, in solving the Navier-Stokes equations, this method links the degree of interpolation polynomials to the order of exact integration. As a result, the mass matrix in inner product form and the flux term matrix cannot be integrated exactly. How significant is this impact? Does it lead to aliasing errors?

[jlchan]

It does lead to some under integration errors, but these decrease rapidly as the polynomial degree increases. Moreover, Trixi's VolumeIntegralFluxDifferencing avoids most under integration-based stability issues.

[teddyz1999]

Understood. Thank you for your response.