The full-discrete mixed finite element methods for nonlinear hyperbolic equations

DOI10.1016/S1007-5704(98)90005-3zbMath0918.65067OpenAlexW2053139767MaRDI QIDQ1288580

Yanping Chen, Yunqing Huang

Publication date: 17 August 1999

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1007-5704(98)90005-3

zbMATH Keywords

convergenceerror estimatesmixed finite element methodssecond-order nonlinear hyperbolic equations

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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)

Domain decomposition and expanded mixed method for parabolic partial differential equations ⋮ Nonlinear wave equation with Dirichlet and acoustic boundary conditions: theoretical analysis and numerical simulation ⋮ Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlinear Schrödinger equation ⋮ Superconvergence analysis of a two-grid method for nonlinear hyperbolic equations ⋮ Unconditional superconvergence analysis of a linearized Galerkin FEM for nonlinear hyperbolic equations ⋮ Least-squares Galerkin procedure for second-order hyperbolic equations ⋮ Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element ⋮ Fast L2-1\(_\sigma\) Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives ⋮ Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation ⋮ A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation ⋮ Superconvergence of the split least‐squares method for second‐order hyperbolic equations

Cites Work

• A priori estimates for mixed finite element methods for the wave equation
• Global Estimates for Mixed Methods for Second Order Elliptic Equations
• A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
• $L^\infty $-Error Estimates for Mixed Methods for Semilinear Second-Order Elliptic Equations
• Improved error estimates for mixed finite‐element approximations for nonlinear parabolic equations: The continuous‐time case
• Improved error estimates for mixed finite‐element approximations for nonlinear parabolic equations: The discrete‐time case
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