Well-Balanced Second-Order Approximation of the Shallow Water Equation with Continuous Finite Elements

DOI10.1137/17M1122463zbMath1459.65165MaRDI QIDQ4602351

Bojan Popov, Pascal Azerad, Jean-Luc Guermond

Publication date: 10 January 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

finite element methodsecond-order methodshallow waterpositivity preservinginvariant domainwell-balanced approximation

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial-boundary value problems for first-order hyperbolic systems (35L50) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (13)

A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere ⋮ Well-Balanced Second-Order Finite Element Approximation of the Shallow Water Equations with Friction ⋮ Well-balanced second-order convex limiting technique for solving the Serre-Green-Naghdi equations ⋮ SUPG formulation augmented with YZβ shock‐capturing for computing shallow‐water equations ⋮ A comparative study of iterative Riemann solvers for the shallow water and Euler equations ⋮ Application of a limiterless quasi acoustic scheme to solve two-dimensional shallow water equations with an uneven bottom ⋮ New directional vector limiters for discontinuous Galerkin methods ⋮ Robust explicit relaxation technique for solving the Green-Naghdi equations ⋮ Convergence of a Second-order Energy-decaying Method for the Viscous Rotating Shallow Water Equation ⋮ Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems ⋮ A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves ⋮ Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws ⋮ Improvement of the hydrostatic reconstruction scheme to get fully discrete entropy inequalities

Uses Software

• SWASHES

Cites Work

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