Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations

By Clint N. Dawson, Jennifer Proft. 2002

73 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A Survey of High Order Schemes for the Shallow Water Equations (2014, background): “Several advantages of the DGmethod, including its high order accuracy, high parallel efficiency, flexibility for hp-adaptivity and arbitrary geometry and meshes, make it suited for the SWEs, see [16, 19, 23, 38, 51].”
hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow (2006, background): “Although no theoretical convergence rates are known for DG methods that incorporate complex numerical fluxes (such as the HLLC or Roe flux) applied to the fully nonlinear SWE without eddy viscosity, previous numerical results using hp DG methods have shown h-convergence rates of p+1 and exponential ”
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes (2011, methodology): “In recent years, FE methods based on discretizing the primitive form of the SW equations using discontinuous approximating spaces have also been studied [1,2,15,18].”
Continuous, discontinuous and coupled discontinuous–continuous Galerkin finite element methods for the shallow water equations (2006, methodology): “Note that only the DG method has the advantage of weak boundary conditions that do not a ect accuracy of both the continuity and momentum equations as veri ed in References [38, 45].”