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In this paper we propose a novel regularization strategy for the localdiscontinuous Galerkin method to solve the Hamilton-Jacobi equation in thecontext of level-set reinitialization. The novel regularization idea works inanalogy to shock-capturing schemes for discontinuous Galerkin methods, whichare based on finite volume sub-cells. In this spirit, the local discontinuousGalerkin method is combined with an upwind/downwind finite volume sub-celldiscretization, which is applied in areas of low regularity. To ensure theapplicability on unstructured meshes, the finite volume discretization is basedon a least squares approach.

A novel regularization strategy for the local discontinuous Galerkin method for level-set reinitialization