4
$\begingroup$

Quadrature-free DG method using nodal Lagrangian basis are computationally very efficient. I have seen many papers using this method for linear PDE but almost no literature for non-linear PDE like compressible Euler equations. The book of Hesthaven & Warburton discusses this and talks of errors in quadrature-free method for non-linear problems and the need to use some filter. The few papers I have seen on quadrature-free method like this one use the same degree basis for solution and flux and dont seem to use any filter (but they have artificial viscosity which is probably enough). I would like to ask the experts if there are any issues in using quadrature-free approach for non-linear problems when I am already using a non-linear limiter or artificial viscosity ? Do they give the same convergence rates as the quadrature-based methods ?

$\endgroup$
0
$\begingroup$

I think this paper by H.L. Atkins and C.-W. Shu is exactly what you are looking for:

Quadrature-Free Implementation of Discontinuous Galerkin Method for Hyperbolic Equations

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.