Nonlinear Galerkin finite element methods for fourth-order bi-flux diffusion model with nonlinear reaction term

DOI10.1007/s40314-020-01168-wzbMath1449.65247OpenAlexW3028010004MaRDI QIDQ2185038

Maosheng Jiang, Jiang Zhu, Luiz Bevilacqua, Xi-Jun Yu

Publication date: 4 June 2020

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

Full work available at URL: https://doi.org/10.1007/s40314-020-01168-w

zbMATH Keywords

numerical experimentsnonlinear Galerkin methodreaction diffusionbi-flux diffusionHermite element

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (2)

Numerical method for solving the fractional evolutionary model of bi-flux diffusion processes ⋮ Unconditional superconvergence analysis for the nonlinear bi-flux diffusion equation

Cites Work

• Unnamed Item
• A combined discontinuous Galerkin finite element method for miscible displacement problem
• A new nonlinear Galerkin finite element method for the computation of reaction diffusion equations
• Nonlinear Galerkin methods: The finite elements case
• Orthogonal cubic spline collocation method for the extended Fisher--Kolmogorov equation
• Incremental unknowns, multilevel methods and the numerical simulation of turbulence
• Chaotic spatial patterns described by the extended Fisher-Kolmogorov equation
• Bi-flux theory applied to the dispersion of particles in anisotropic substratum
• Implementation of finite element nonlinear Galerkin methods using hierarchical bases
• Finite difference discretization of the extended Fisher-Kolmogorov equation in two dimensions
• A nonlinear Galerkin method: The two-level Fourier-collocation case
• Periodic solutions for extended Fisher-Kolmogorov and Swift-Hohenberg equations obtained using a continuation theorem
• Numerical Studies of the Cahn-Hilliard Equation for Phase Separation
• Pattern formation in the one-dimensional Gray - Scott model
• Numerical Analysis of a Continuum Model of Phase Transition
• Spatial Patterns Described by the Extended Fisher--Kolmogorov Equation: Periodic Solutions
• Numerical methods for the rosenau equation
• The chemical basis of morphogenesis
• Nonlinear Galerkin Methods
• Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
• High-order finite element methods for the Kuramoto-Sivashinsky equation

This page was built for publication: Nonlinear Galerkin finite element methods for fourth-order bi-flux diffusion model with nonlinear reaction term