Finite volume element method with interpolated coefficients for two-point boundary value problem of semilinear differential equations

DOI10.1016/j.cma.2006.10.042zbMath1173.65329OpenAlexW2057969389MaRDI QIDQ1033396

Yanping Chen, Zhiguang Xiong

Publication date: 6 November 2009

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2006.10.042

zbMATH Keywords

two-point boundary value problemsemilinear differential equationfinite volume element with interpolated coefficients

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (9)

A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations ⋮ \(P _{1}\)-nonconforming quadrilateral finite volume methods for the semilinear elliptic equations ⋮ A rectangular finite volume element method for a semilinear elliptic equation ⋮ Interpolated coefficient characteristic finite element method for semilinear convection-diffusion optimal control problems ⋮ Error estimates of fully discrete mixed finite element methods for semilinear quadratic parabolic optimal control problem ⋮ A fifth order accurate geometric mesh finite difference method for general nonlinear two point boundary value problems ⋮ A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation ⋮ Interpolation coefficients mixed finite element methods for general semilinear Dirichlet boundary elliptic optimal control problems ⋮ Convergence of the interpolated coefficient finite element method for the two-dimensional elliptic sine-Gordon equations

Cites Work

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• The node-centred finite volume approach: Bridge between finite differences and finite elements
• On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids
• Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation
• Convergence of Finite Volume Schemes for Poisson’s Equation on Nonuniform Meshes
• The Accuracy of Cell Vertex Finite Volume Methods on Quadrilateral Meshes
• Asymptotic $L^\infty $-Error Estimates for Linear Finite Element Approximations of Quasilinear Boundary Value Problems
• Error Estimates of Optimal Order for Finite Element Methods with Interpolated Coefficients for the Nonlinear Heat Equation
• Finite Volume Methods for Elliptic PDE's: A New Approach
• Equivalent Norms for Sobolev Spaces

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