Construction and Analysis of HDG Methods for Linearized Shallow Water Equations

DOI10.1137/16M1057243zbMath1457.65098MaRDI QIDQ2953218

Tan Bui-Thanh

Publication date: 4 January 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergencewell-posednessshallow water equationdiscontinuous Galerkin methodsGodunov methodLax-Friedrichs fluxupwindhybridized discontinuous Galerkin methodsRiemann fluxupwind hybridized discontinuous Galerkin methods

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (12)

A multilevel approach for trace system in HDG discretizations ⋮ Multigrid preconditioners for the hybridised discontinuous Galerkin discretisation of the shallow water equations ⋮ An improved iterative HDG approach for partial differential equations ⋮ Hybridizable discontinuous Galerkin method with mixed-order spaces for nonlinear diffusion equations with internal jumps ⋮ iHDG: An Iterative HDG Framework for Partial Differential Equations ⋮ IMEX HDG-DG: a coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for shallow water systems ⋮ Superconvergent HDG methods for Maxwell's equations via the \(M\)-decomposition ⋮ A hybridized discontinuous Galerkin method for a linear degenerate elliptic equation arising from two-phase mixtures ⋮ An explicit hybridized discontinuous Galerkin method for Serre-Green-Naghdi wave model ⋮ HDG-POD reduced order model of the heat equation ⋮ Unified Geometric Multigrid Algorithm for Hybridized High-Order Finite Element Methods ⋮ A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media

Uses Software

• HE-E1GODF

Cites Work

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