Dmitri Kuzmin Slope limiting for discontinuous Galerkin approximations with a possibly non-orthogonal Taylor basis International Journal for Numerical Methods in Fluids 71
This paper presents a new predictor-corrector approach to hierarchical slope limiting in high-order discontinuous Galerkin methods on the basis of explicit Runge-Kutta time-stepping. In the case of a non-orthogonal Taylor basis, the off-diagonal part of the element mass matrix is preconstrained by limiting the spatial variations of the discretized time derivatives. This mass lumping strategy is shown to produce a marked improvement for P1 and P2 approximations on triangular meshes.
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