\(H^1\)-Galerkin mixed finite element method for the regularized long wave equation

DOI10.1007/s00607-005-0158-7zbMath1098.65096OpenAlexW2057616362MaRDI QIDQ2492667

Ling Guo, Huan-Zhen Chen

Publication date: 14 June 2006

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-005-0158-7

zbMATH Keywords

Galerkin methodnumerical resultsregularized long wave equationoptimal error estimatesmixed finite element methodsolitary wave solutionsshallow water wavesbackward Euler schemenonlinear dispersive wavesLadyshenskaya-Babuška-Brezzi consistency conditionion acoustic plasma waves

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) 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) Soliton equations (35Q51) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Higher-order nonlinear hyperbolic equations (35L75)

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Cites Work

• A priori estimates for mixed finite element methods for the wave equation
• Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics
• Numerical schemes for a model for nonlinear dispersive waves
• Two families of mixed finite elements for second order elliptic problems
• Mixed finite elements for second order elliptic problems in three variables
• Petrov-Galerkin methods for nonlinear dispersive waves
• Numerical study of the regularized long-wave equation. I: Numerical methods
• Numerical study of the regularized long-wave equation. II: Interaction of solitary waves
• Galerkin methods applied to some model equations for non-linear dispersive waves
• Error estimates for a Galerkin method for a class of model equations for long waves
• Solitary waves of the regularised long-wave equation
• Iterative solution of the stream function-vorticity equations using a multigrid solver with finite elements
• Error estimates for mixed finite element methods for nonlinear parabolic problems
• Mixed Finite Element Analysis and Numerical Solitary Solution for the RLW Equation
• A B‐spline finite element method for the regularized long wave equation
• AnH¹-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations
• H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations
• A least-squares finite element scheme for the RLW equation

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