Nonlinear Galerkin finite element method applied to the system of reaction-diffusion equations in one space dimension

DOI10.1016/j.camwa.2017.02.032zbMath1373.65071OpenAlexW2596609764MaRDI QIDQ2403734

Jan Mach, Michal Beneš, Pavel Strachota

Publication date: 12 September 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.02.032

zbMATH Keywords

convergencecomparison of methodsfinite element methodfinite difference methodevolution equationnumerical examplesnonlinear Galerkin methodreaction-diffusion systemRunge-Kutta methodcomputational efficiency

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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) Complexity and performance of numerical algorithms (65Y20) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (2)

Mathematical model of signal propagation in excitable media ⋮ Nonlinear Galerkin methods for a system of PDEs with Turing instabilities

Cites Work

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• Approximate inertial manifolds for reaction-diffusion equations in high space dimension
• Nonlinear Galerkin methods: The finite elements case
• Geometric theory of semilinear parabolic equations
• Nonlinear Galerkin method and subgrid-scale model for two-dimensional turbulent flows
• Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method
• Nonlinear Galerkin method in the finite difference case and wavelet-like incremental unknowns
• Full discrete nonlinear Galerkin method for the Navier-Stokes equations
• Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations
• Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
• A second order operator splitting method for Allen-Cahn type equations with nonlinear source terms
• Geometrical image segmentation by the Allen-Cahn equation
• The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows
• Implementation of finite element nonlinear Galerkin methods using hierarchical bases
• Pattern formation in the Gray-Scott model
• Numerical solution of ordinary simultaneous differential equations of the 1st order using a method for automatic step change
• A nonlinear Galerkin method: The two-level Fourier-collocation case
• Asymmetric Spotty Patterns for the Gray-Scott Model in R2
• Modelling of the interaction of small and large eddies in two dimensional turbulent flows
• Pattern formation in the one-dimensional Gray - Scott model
• Nonlinear Galerkin Methods
• Time integration of the non-linear Galerkin method
• Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
• Galerkin Finite Element Methods for Parabolic Problems
• Pattern formations in two-dimensional Gray-Scott model: Existence of single-spot solutions and their stability
• Mathematical analysis of phase-field equations with numerically efficient coupling terms
• Spatio-temporal chaos for the Gray-Scott model
• Nonlinear Galerkin method for reaction-diffusion systems admitting invariant regions

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