Lumped finite elements for reaction-cross-diffusion systems on stationary surfaces

DOI10.1016/j.camwa.2017.07.044zbMath1397.65185arXiv1609.02741OpenAlexW2752638378MaRDI QIDQ1672659

Ivonne Sgura, Anotida Madzvamuse, Massimo Frittelli, Chandrasekhar Venkataraman

Publication date: 11 September 2018

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

Full work available at URL: https://arxiv.org/abs/1609.02741

zbMATH Keywords

convergence analysispattern formationmass lumpinginvariant regionsurface finite elementsreaction-cross-diffusion

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (11)

Numerical preservation of velocity induced invariant regions for reaction-diffusion systems on evolving surfaces ⋮ Virtual Element Method for the Laplace-Beltrami equation on surfaces ⋮ Virtual element method for elliptic bulk‐surface PDEs in three space dimensions ⋮ Unconditionally maximum principle preserving finite element schemes for the surface Allen–Cahn type equations ⋮ A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration ⋮ Numerical simulations for the chemotaxis models on surfaces via a novel characteristic finite element method ⋮ A positivity preserving characteristic finite element method for solving the transport and convection-diffusion-reaction equations on general surfaces ⋮ Matrix-oriented discretization methods for reaction-diffusion PDEs: comparisons and applications ⋮ Global existence of solutions for an \(m\)-component cross-diffusion system with a 3-component case study ⋮ Unnamed Item ⋮ Comparison of a finite-element and finite-volume scheme for a degenerate cross-diffusion system for ion transport

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