Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations

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Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations (2009, methodology): “2 The Kuramoto-Sivashinsky type equations In [99], an LDG method has been developed to solve the Kuramoto-Sivashinsky type equations ut+ f (u)x−(a(u)ux)x+(r (u)g(r(u)x)x)x+(s(ux)uxx)xx =0, (3.”
High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations on Unstructured Hexahedral Grids (2006, methodology): “One approach is given in [17], and is named the average approach, and the other approach is a local DG-like approach [9, 40].”
Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments (2014, methodology): “LDG methods are developed in [93] to solve the Kuramoto-Sivashinsky type equations”
Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems (2016, methodology): “The LDG schemes have also been successfully designed for other diffusion problems, for example, the bi-harmonic equations [9, 23], the Kuramoto–Sivashinsky type equations [20], the Cahn–Hilliard equation [19], etc.”