Optimal energy conserving and energy dissipative local discontinuous Galerkin methods for the Benjamin-Bona-Mahony equation

DOI10.1007/s10915-020-01172-6zbMath1436.65143OpenAlexW3015018731MaRDI QIDQ2173571

Yulong Xing, Xiaole Li, Ching-Shan Chou

Publication date: 16 April 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-020-01172-6

zbMATH Keywords

energy conserving methodsoptimal error estimateBenjamin-Bona-Mahony equationlocal discontinuous Galerkin methodsenergy dissipative methods

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Solitary waves for incompressible inviscid fluids (76B25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Nonlinear higher-order PDEs (35G20) 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)

Related Items (11)

On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: energy conservation and multi-symplecticity ⋮ Convergence and stability in maximum norms of linearized fourth-order conservative compact scheme for Benjamin-Bona-Mahony-Burgers' equation ⋮ Local discontinuous Galerkin methods for the \(abcd\) nonlinear Boussinesq system ⋮ L1/LDG method for the generalized time-fractional Burgers equation ⋮ Energy conserving discontinuous Galerkin method with scalar auxiliary variable technique for the nonlinear Dirac equation ⋮ Local discontinuous Galerkin method for a nonlocal viscous water wave model ⋮ A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations ⋮ Local discontinuous Galerkin methods to a dispersive system of KdV-type equations ⋮ Energy conserving local discontinuous Galerkin methods for the improved Boussinesq equation ⋮ A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations ⋮ Local discontinuous Galerkin method combined with the \(L2\) formula for the time fractional cable model

Cites Work

• Unnamed Item
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• Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media
• Energy conserving local discontinuous Galerkin methods for wave propagation problems
• A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect
• A fully-discrete local discontinuous Galerkin method for convection-dominated Sobolev equation
• Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation
• The first integral method for modified Benjamin-Bona-Mahony equation
• The convergence of fully discrete Galerkin approximations for the Benjamin--Bona--Mahony (BBM) equation
• On the convergence of difference schemes for the Benjamin-Bona-Mahony (BBM) equation
• Energy conserving local discontinuous Galerkin methods for the nonlinear Schrödinger equation with wave operator
• Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• Local discontinuous Galerkin method for the Keller-Segel chemotaxis model
• An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-de Vries equation
• Local discontinuous Galerkin methods for the Boussinesq coupled BBM system
• Exact solutions with compact and noncompact structures for the one-dimensional generalized Benjamin-Bona-Mahony equation
• A conservative discontinuous Galerkin method for the Degasperis-Procesi equation
• Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems
• Energy conserving local discontinuous Galerkin methods for the improved Boussinesq equation
• Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations
• $L^2$ stable discontinuous Galerkin methods for one-dimensional two-way wave equations
• Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
• Stability and Error Estimates of Local Discontinuous Galerkin Methods with Implicit-Explicit Time-Marching for Advection-Diffusion Problems
• Application of generalized Gauss–Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• Global existence for the Benjamin-Bona-Mahony equation in arbitrary dimensions
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• On the Benjamin-Bona-Mahony equation in higher dimensions
• The initial-value problem for the Korteweg-de Vries equation
• Existence and Uniqueness for Periodic Solutions of the Benjamin–Bona–Mahony Equation
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Conservative and Dissipative Local Discontinuous Galerkin Methods for Korteweg-de Vries Type Equations
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations
• A Posteriori Error Estimates for Conservative Local Discontinuous GalerkinMethods for the Generalized Korteweg-de Vries Equation
• Finite difference discretization of the Benjamin‐Bona‐Mahony‐Burgers equation
• Model equations for long waves in nonlinear dispersive systems
• An Invariant Preserving Discontinuous Galerkin Method for the Camassa--Holm Equation

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