Superconvergence analysis of the finite element method for nonlinear hyperbolic equations with nonlinear boundary condition

DOI10.1007/s11766-008-1901-6zbMath1199.65317OpenAlexW2042940864MaRDI QIDQ1032810

Zhiyan Li, Dong-Yang Shi

Publication date: 11 November 2009

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-008-1901-6

zbMATH Keywords

finite element methodnonlinear boundary conditionsuperconvergencesemidiscretizationnonlinear hyperbolic equationpostprocessing technique

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (9)

Nonlinear wave equation with Dirichlet and acoustic boundary conditions: theoretical analysis and numerical simulation ⋮ Superconvergence analysis of a two-grid method for nonlinear hyperbolic equations ⋮ Finite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energy ⋮ Polynomial preserving recovery for high frequency wave propagation ⋮ Unconditional superconvergence analysis of a linearized Galerkin FEM for nonlinear hyperbolic equations ⋮ Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element ⋮ Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term ⋮ A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation ⋮ Superconvergence of fully discrete splitting positive definite mixed FEM for hyperbolic equations

Cites Work

• Galerkin methods for parabolic equations with nonlinear boundary conditions
• Superconvergence in the Pressure in the Simulation of Miscible Displacement
• Galerkin Methods for Nonlinear Parabolic Integrodifferential Equations with Nonlinear Boundary Conditions
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