In order to resolve fine features of a numerical solution, run-time mesh refinement might be required. Commonly used refinement strategies aimed at preserving mesh quality result in nonconfirming meshes, i.e. meshes where a larger element might share an edge with two smaller elements. In this talk we will address limiting on such meshes. Limiting is a technique aimed to stabilize a solution in the presence of shocks and steep solution gradients. Limiting on nonconforming meshes is difficult due to lack of structure in the mesh and because most limiting algorithms were developed for conforming meshes.

We present a second-order limiter for the discontinuous Galerkin method on nonconforming triangular meshes that arise in adaptive computations. The limiter modifies the linear solution coefficients (or moments) by reconstructing the slopes along a set of directions in which the moments decouple. The resulting solutions satisfy the local maximum principle (LMP) for scalar problems, i.e. are stable in the maximum norm. We show that our algorithm is efficient for solution of nonlinear hyperbolic systems such as Euler equations and scales well when implemented on GPUs.