Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations.

DOI10.1016/j.cma.2003.09.011zbMath1075.76570OpenAlexW2080697724MaRDI QIDQ1430662

Jennifer Proft, Clint N. Dawson

Publication date: 27 May 2004

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2003.09.011

zbMATH Keywords

Galerkin finite element methodDiscontinuous Galerkin methodShallow water equationsCoupled method

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10) Waves for incompressible viscous fluids (76D33)

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Uses Software

• ADCIRC

Cites Work

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• Compatible algorithms for coupled flow and transport
• An analysis of the wave equation model for finite element tidal computations
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• A wave equation model for finite element tidal computations
• A Godunov-type finite volume method for the system of shallow water equations
• A discontinuous \(hp\) finite element method for diffusion problems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• A discontinuous \(hp\) finite element method for convection-diffusion problems
• Aspects of nonlinear simulations using shallow-water models based on the wave continuity equation
• \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws
• A characteristic-Galerkin approximation to a system of shallow water equations
• Coupling of continuous and discontinuous Galerkin methods for transport problems
• Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations
• Conservative, shock-capturing transport methods with nonconservative velocity approximations
• Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
• An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
• A priori error estimates for interior penalty versions of the local discontinuous Galerkin method applied to transport equations
• Finite Element Collocation Methods for First Order Systems
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Finite Element Approximations to the System of Shallow Water Equations, Part II: Discrete-Time A Priori Error Estimates
• Finite Element Approximations to the System of Shallow Water Equations I: Continuous-Time A Priori Error Estimates
• Grid convergence studies for the prediction of hurricane storm surge
• A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems