Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller--Segel and Poisson--Nernst--Planck Equations

DOI10.1137/20M1365417MaRDI QIDQ4997384

Fukeng Huang, Jie Shen

Publication date: 29 June 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

dissipative systemsPoisson-Nernst-Planckenergy stabilityKeller-SegelSAV approachpositivity or bound preserving

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Direct numerical methods for linear systems and matrix inversion (65F05) Cell movement (chemotaxis, etc.) (92C17) Electrochemistry (78A57) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

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Uses Software

• Chemotaxis

Cites Work

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• Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis
• \{Euclidean, metric, and Wasserstein\} gradient flows: an overview
• Initiation of slime mold aggregation viewed as an instability
• The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
• A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
• A user's guide to PDE models for chemotaxis
• Convergent discretizations for the Nernst-Planck-Poisson system
• On the basic equations for carrier transport in semiconductors
• The scalar auxiliary variable (SAV) approach for gradient flows
• A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems
• Upwind-difference potentials method for Patlak-Keller-Segel chemotaxis model
• A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson-Nernst-Planck equations
• Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations
• A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
• Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
• The Variational Formulation of the Fokker--Planck Equation
• Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations
• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
• Point Dynamics in a Singular Limit of the Keller--Segel Model 1: Motion of the Concentration Regions
• Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions
• Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller--Segel Equations
• A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
• New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model
• The Keller--Segel Model with Logistic Sensitivity Function and Small Diffusivity
• Global existence for a parabolic chemotaxis model with prevention of overcrowding