The discontinuous Galerkin finite element method for the 2D shallow water equations

DOI10.1016/S0378-4754(01)00277-4zbMath0987.76054OpenAlexW2025190703MaRDI QIDQ5939975

Hong Li, Ru-xun Liu

Publication date: 27 June 2002

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-4754(01)00277-4

zbMATH Keywords

circular damfree-surface problemhigh-order finite element methodhydraulic dynamicsirregular domainregular domainstructured rectangular meshtotal variational diminishing Runge-Kutta discontinuous Galerkin methodunstructured triangular mesh

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (13)

An hp-adaptive discontinuous Galerkin method for shallow water flows ⋮ \textit{A posteriori} finite-volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equations ⋮ Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms ⋮ A performance comparison of continuous and discontinuous finite element shallow water models ⋮ A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying ⋮ A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations ⋮ Hp discontinuous Galerkin methods for advection dominated problems in shallow water flow ⋮ High-order discontinuous Galerkin methods for coastal hydrodynamics applications ⋮ High-order semi-implicit time-integrators for a triangular discontinuous Galerkin oceanic shallow water model ⋮ Discontinuous Galerkin spectral/\(hp\) element modelling of dispersive shallow water systems ⋮ An improved meshless artificial viscosity technology combined with local radial point interpolation method for 2D shallow water equations ⋮ A high-order embedded domain method combining a predictor-corrector-Fourier-continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex domains ⋮ An a priori error estimate for the local discontinuous <scp>G</scp>alerkin method applied to two‐dimensional shallow water and morphodynamic flow

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