Sub-Cell Shock Capturing for Discontinuous Galerkin Methods

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A Parameter-Free Generalized Moment Limiter for High- Order Methods on Unstructured Grids (2009, background): “High-order limiters based on artificial viscosity have also been investigated by various researchers [13,26].”
Comparisons of p-adaptation strategies based on truncation- and discretisation-errors for high order discontinuous Galerkin methods (2016, methodology): “Extension to high order methods [31, 34, 3] may use the polynomial energy decay for each mode (that 50”
A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids (2014, neutral): “Introduction The discontinuous Galerkin (DG) methods [1–26] have recently become popular for the solution of systems of conservation laws.”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “According to numerical evidence provided in [17] for the one-dimensional case, the artificial viscosity approach [79] seems to be more appropriate for capturing subcell features compared to other DG limiters, especially for very high polynomial degrees N.”