All the papers I have seen on DG methods for hyperbolic conservation laws together with limiters to compute discontinuous solutions make use of Taylor polynomial basis (Pk basis) or Legendre polynomials. In these cases, limiters have been developed. But if I want to use nodal basis on quadrilaterals/rectangles, then I have not seen any papers which develop limiters for this case. My attempts at writing a nodal DG code and extending the existing limiters in a natural way does not lead to accurate solutions. So I am looking for any existing literature that uses nodal DG (Qk basis) on quadrilaterals and limiters to compute discontinuous solutions.Thankspraveen
Nodal DG method and limiters for hyperbolic conservation laws
discontinuous galerkin