Transparent boundary conditions for the shallow water equations with a mixed finite element formulation

DOI10.1016/S0168-9274(02)00140-XzbMath1023.76021MaRDI QIDQ1861978

Ivar Lie, Astrid Holstad

Publication date: 10 March 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

shallow water equationsmixed finite element methodincoming wavescharacteristic-based transparent boundary conditionsoutgoing wavessemi-Lagrangian time discretization

Mathematics Subject Classification ID

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

Uses Software

• LAPACK

Cites Work

• Numerical solution of problems on unbounded domains. A review
• Control-volume mixed finite element methods
• A new family of mixed finite element spaces over rectangles
• Recent developments in the numerical simulation of shallow water equations. I: Boundary conditions
• The final NETLIB-LP results
• A characteristic-Galerkin approximation to a system of shallow water equations
• Existence theorem for the solution of a shallow water problem
• Efficient rectangular mixed finite elements in two and three space variables
• Finite Element Methods for Navier-Stokes Equations
• On Convergence of Block-Centered Finite Differences for Elliptic Problems
• Stability of the Lagrange-Galerkin method with non-exact integration
• Mixed and Hybrid Finite Element Methods
• Mixed-hybrid finite elements and streamline computation for the potential flow problem
• Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
• A Galerkin-Characteristic Algorithm for Transport-Diffusion Equations
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
• A finite element method for 3D hydrostatic water flows
• Well-posed transparent boundary conditions for the shallow water equations
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