Convergence of FEM with interpolated coefficients for semilinear hyperbolic equation

DOI10.1016/j.cam.2007.02.023zbMath1148.65079OpenAlexW2018670777MaRDI QIDQ2479390

Zhiguang Xiong, Yanping Chen, Yan Zhang

Publication date: 26 March 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.02.023

zbMATH Keywords

convergenceerror estimatesfinite element methodsemilinear hyperbolic equationsinterpolated coefficients

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 (9)

A SPLITTING METHOD FOR THE CAHN–HILLIARD EQUATION WITH INERTIAL TERM ⋮ Superconvergent interpolatory HDG methods for reaction diffusion equations. II: HHO-inspired methods ⋮ The improved element-free Galerkin method for three-dimensional wave equation ⋮ Nonlinear model reduction based on the finite element method with interpolated coefficients: Semilinear parabolic equations ⋮ Meshless local Petrov-Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation ⋮ Superconvergence of a discontinuous finite element method for a nonlinear ordinary differential equation ⋮ On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three-dimensional wave equations ⋮ Superconvergent interpolatory HDG methods for reaction diffusion equations. I: An \(HDG_k\) method ⋮ Interpolatory HDG method for parabolic semilinear PDEs

Cites Work

• Superconvergence of rectangular finite element with interpolated coefficients for semilinear elliptic problem
• Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations
• A second order finite difference analog of the first biharmonic boundary value problem
• Simplified continuous finite element method for a class of nonlinear oscillating equations
• Semidiscrete and single step fully discrete approximations for second order hyperbolic equations with time-dependent coefficients
• Higher Order Single Step Fully Discrete Approximations for Second Order Hyperbolic Equations with Time Dependent Coefficients
• Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation
• Cosine Methods for Nonlinear Second-Order Hyperbolic Equations
• On multistep-Galerkin discretizations of semilinear hyperbolic and parabolic equations
• Error Estimates of Optimal Order for Finite Element Methods with Interpolated Coefficients for the Nonlinear Heat Equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Convergence of FEM with interpolated coefficients for semilinear hyperbolic equation