Numerical and theoretical study of weak Galerkin finite element solutions of Turing patterns in reaction–diffusion systems
DOI10.1002/num.22529OpenAlexW3081062443MaRDI QIDQ6088451
Rezvan Salehi, Leila Jafarian Khaled-Abad
Publication date: 14 December 2023
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.22529
reaction-diffusion systemserror estimateweak gradientweak Galerkin finite element methodstability and convergence of numerical methods
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) Chemically reacting flows (80A32) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Pattern formations in context of PDEs (35B36)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation
- A robust DPG method for convection-dominated diffusion problems. II: Adjoint boundary conditions and mesh-dependent test norms
- Weak Galerkin methods for second order elliptic interface problems
- Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion
- Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity
- Projected finite elements for reaction-diffusion systems on stationary closed surfaces
- A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order
- A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods
- Reaction and diffusion on growing domains: scenarios for robust pattern formation
- A weak Galerkin finite element method for the Maxwell equations
- Best uniform polynomial approximation of some rational functions
- The use of element free Galerkin method based on moving Kriging and radial point interpolation techniques for solving some types of Turing models
- Weak Galerkin methods for time-dependent Maxwell's equations
- A weak Galerkin finite element method for a coupled Stokes-Darcy problem on general meshes
- The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes
- Adaptive moving mesh computations for reaction--diffusion systems
- A weak Galerkin finite element method for second-order elliptic problems
- Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
- A weak Galerkin finite element method with polynomial reduction
- A weak Galerkin finite element method for the Oseen equations
- A computational study of the weak Galerkin method for second-order elliptic equations
- An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes
- The finite volume spectral element method to solve Turing models in the biological pattern formation
- Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains
- A comparative study on the weak Galerkin, discontinuous Galerkin, and mixed finite element methods
- The finite element method for elliptic equations with discontinuous coefficients
- On numerical improvement of Gauss--Radau quadrature rules
- A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains
- A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations
- Weak Galerkin finite element methods for Parabolic equations
- On L<sup>2</sup> Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems
- A new weak Galerkin finite element method for the Helmholtz equation
- Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type
- Analysis of the DPG Method for the Poisson Equation
- A weak Galerkin mixed finite element method for second order elliptic problems
- Weak Galerkin Finite Element Methods on Polytopal Meshes
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- Finite Element Methods for Elliptic Equations Using Nonconforming Elements
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- The chemical basis of morphogenesis
- A Weak Galerkin Finite Element Method for the Linear Elasticity Problem in Mixed Form
- Weak Galerkin method for the coupled Darcy–Stokes flow
- A weak Galerkin finite element method for a coupled Stokes‐Darcy problem
- A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation
- A New Weak Galerkin Finite Element Scheme for the Brinkman Model
- Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
- Spectral Methods
- Three Matlab Implementations of the Lowest-order Raviart-Thomas Mfem with a Posteriori Error Control