Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller--Segel Equations

DOI10.1137/19M1246705zbMath1440.65101OpenAlexW3029281960MaRDI QIDQ5113126

Jie Shen, Jie Xu

Publication date: 10 June 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1246705

zbMATH Keywords

chemotaxisKeller-Segel equationsenergy stabilitygradient flowsbound preserving

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) 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) Computational methods for problems pertaining to biology (92-08) Cell movement (chemotaxis, etc.) (92C17) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (18)

Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation ⋮ Fully decoupled and energy stable BDF schemes for a class of Keller-Segel equations ⋮ Error estimates for the finite element method of the chemotaxis-Navier-Stokes equations ⋮ An unconditionally energy stable and positive upwind DG scheme for the Keller-Segel model ⋮ Unconditionally energy-stable discontinuous Galerkin method for the chemo-repulsion-Navier-Stokes system ⋮ A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions ⋮ Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes ⋮ High-order finite difference approximation of the Keller-Segel model with additional self- and cross-diffusion terms and a logistic source ⋮ Unconditionally energy-stable finite element scheme for the chemotaxis-fluid system ⋮ Unconditional stability of first and second orders implicit/explicit schemes for the natural convection equations ⋮ A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model ⋮ Bound/positivity preserving SAV schemes for the Patlak-Keller-Segel-Navier-Stokes system ⋮ Unnamed Item ⋮ Unconditionally maximum bound principle preserving linear schemes for the conservative Allen-Cahn equation with nonlocal constraint ⋮ Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations ⋮ A Convergent Entropy Diminishing Finite Volume Scheme for a Cross-Diffusion System ⋮ Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller--Segel and Poisson--Nernst--Planck Equations ⋮ \(Q\)-tensor gradient flow with quasi-entropy and discretizations preserving physical constraints

Uses Software

• Chemotaxis

Cites Work

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