Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations

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Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems (2016, methodology): “The semi-discrete LDG scheme The semi-discrete LDG scheme [6, 21] starts from the following equivalent first-order differential system Ut + ∇ · (F (U) −Q) = 0, Q−∇U = 0, (x, t) ∈ QT , (2.”
Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems (2019, background): “The “hat” terms are numerical fluxes which are taken as in [12, 27, 26]”