Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces

DOI10.4208/cicp.OA-2016-0029zbMath1488.65460OpenAlexW2549057225MaRDI QIDQ5158717

Anotida Madzvamuse, Necibe Tuncer

Publication date: 26 October 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/cicp.oa-2016-0029

zbMATH Keywords

pattern formationreaction-diffusion systemsevolving surfacesnon-autonomous partial differential equationsprojected finite elementstime-dependent projection operatorsTuring \textit{diffusively-driven} instability

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) Developmental biology, pattern formation (92C15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Semilinear parabolic equations (35K58) Pattern formations in context of PDEs (35B36)

Related Items (4)

Numerical preservation of velocity induced invariant regions for reaction-diffusion systems on evolving surfaces ⋮ Influence of curvature, growth, and anisotropy on the evolution of Turing patterns on growing manifolds ⋮ Analysis and Simulations of Coupled Bulk-surface Reaction-Diffusion Systems on Exponentially Evolving Volumes ⋮ A surface moving mesh method based on equidistribution and alignment

Cites Work

• Unnamed Item
• Unnamed Item
• Characterization of Turing diffusion-driven instability on evolving domains
• Projected finite elements for reaction-diffusion systems on stationary closed surfaces
• An Eulerian approach to transport and diffusion on evolving implicit surfaces
• Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains
• The surface finite element method for pattern formation on evolving biological surfaces
• Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion
• Eulerian finite element method for parabolic PDEs on implicit surfaces
• Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
• A moving grid finite element method applied to a model biological pattern generator
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Level set methods and dynamic implicit surfaces
• Whole cell tracking through the optimal control of geometric evolution laws
• Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains
• Fourth order partial differential equations on general geometries
• A Lagrangian particle level set method
• Implicit--Explicit Timestepping with Finite Element Approximation of Reaction--Diffusion Systems on Evolving Domains
• A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes
• The Implicit Closest Point Method for the Numerical Solution of Partial Differential Equations on Surfaces
• Numerical computation of advection and diffusion on evolving diffuse interfaces
• Computation of geometric partial differential equations and mean curvature flow
• Finite elements on evolving surfaces
• Radially Projected Finite Elements
• Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
• Simple computation of reaction–diffusion processes on point clouds
• Finite element methods for surface PDEs

This page was built for publication: Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces