Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
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Publication:6071825
DOI10.1137/21m1458247zbMath1527.65082arXiv2111.04722MaRDI QIDQ6071825
Publication date: 29 November 2023
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.04722
hyperbolic conservation lawsnonlinear constraintsgeometric quasilinearizationbound-preserving numerical schemesconvex invariant regionstime-dependent PDE systems
PDEs in connection with fluid mechanics (35Q35) Finite difference methods applied to problems in fluid mechanics (76M20) Finite volume methods applied to problems in fluid mechanics (76M12) Gas dynamics (general theory) (76N15) Hyperbolic conservation laws (35L65) 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) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Euler equations (35Q31) Finite volume methods for boundary value problems involving PDEs (65N08)
Related Items (3)
A New Discretely Divergence-Free Positivity-Preserving High-Order Finite Volume Method for Ideal MHD Equations ⋮ High-order accurate entropy stable schemes for relativistic hydrodynamics with general Synge-type equation of state ⋮ Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics
Cites Work
- Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller--Segel Equations
- On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
- Arbitrarily High-Order Exponential Cut-Off Methods for Preserving Maximum Principle of Parabolic Equations
- Positivity Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations
- A Second-Order Positivity-Preserving Finite Volume Scheme for Diffusion Equations on General Meshes
- High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations
- Positivity-Preserving Finite Difference Weighted ENO Schemes with Constrained Transport for Ideal Magnetohydrodynamic Equations
- Convex and Discrete Geometry
- Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence
- Bound-Preserving Discontinuous Galerkin Method for Compressible Miscible Displacement in Porous Media
- Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations
- Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems
- Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness
- Convex functions and their applications. A contemporary approach
- Positivity-preserving analysis of explicit and implicit Lax-Friedrichs schemes for compressible Euler equations
- Analysis of shear layers in a fluid with temperature-dependent viscosity.
- On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the maximum principle preserving schemes for the generalized Allen-Cahn equation
- Positivity-preserving Lagrangian scheme for multi-material compressible flow
- A realizability-preserving discontinuous Galerkin method for the \(M_1\) model of radiative transfer
- Positivity-preserving method for high-order conservative schemes solving compressible Euler equations
- Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes
- A minimum entropy principle of high order schemes for gas dynamics equations
- A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
- Locally divergence-free discontinuous Galerkin methods for MHD equations
- A minimum entropy principle in the gas dynamics equations
- Failsafe flux limiting and constrained data projections for equations of gas dynamics
- On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
- Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms
- Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations
- High order parametrized maximum-principle-preserving and positivity-preserving WENO schemes on unstructured meshes
- On the monotonicity and discrete maximum principle of the finite difference implementation of \(C^0\)-\(Q^2\) finite element method
- A projection algorithm on the set of polynomials with two bounds
- On maximum-principle-satisfying high order schemes for scalar conservation laws
- A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
- Invariant sets and existence theorems for semilinear parabolic and elliptic systems
- Persistence of invariant sets for dissipative evolution equations
- Gas-kinetic schemes for the compressible Euler equations: Positivity-preserving analysis
- A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
- Constraint preserving integrators for general nonlinear higher index DAEs
- Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
- Globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamic equations
- Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems
- Positivity-preserving high-order discontinuous Galerkin schemes for ten-moment Gaussian closure equations
- Local discontinuous Galerkin method for the Keller-Segel chemotaxis model
- Runge-Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics
- On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations
- Bound-preserving high-order schemes for hyperbolic equations: survey and recent developments
- On discrete maximum principles for discontinuous Galerkin methods
- Positivity of flux vector splitting schemes
- On positivity preserving finite volume schemes for Euler equations
- Arbitrary high-order, conservative and positivity preserving Patankar-type deferred correction schemes
- Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
- Second-order invariant domain preserving approximation of the compressible Navier-Stokes equations
- Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations
- Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations
- A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations
- Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations
- Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation
- Physical-constraints-preserving Lagrangian finite volume schemes for one- and two-dimensional special relativistic hydrodynamics
- Positivity-preserving finite difference WENO scheme for ten-moment equations with source term
- Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations
- Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes
- High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
- Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics
- Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws
- Positivity-preserving DG and central DG methods for ideal MHD equations
- A trapping principle and convergence result for finite element approximate solutions of steady reaction/diffusion systems
- Maximum principle and uniform convergence for the finite element method
- Parametrized positivity preserving flux limiters for the high order finite difference WENO scheme solving compressible Euler equations
- A new Lagrange multiplier approach for constructing structure preserving schemes. I: Positivity preserving
- Strong Stability-Preserving High-Order Time Discretization Methods
- A Positivity-Preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
- High Order Positivity-Preserving Discontinuous Galerkin Methods for Radiative Transfer Equations
- Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations
- Maximum-Principle-Satisfying Third Order Discontinuous Galerkin Schemes for Fokker--Planck Equations
- A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model
- Bound-Preserving High-Order Schemes
- Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
- Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations
- Positivity preserving finite element approximation
- Positivity-Preserving Analysis of Numerical Schemes for Ideal Magnetohydrodynamics
- Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
- Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem
- Invariant Regions for Systems of Conservation Laws
- Second-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions
- Maximum Principle on the Entropy and Second-Order Kinetic Schemes
- Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
- On the Choice of Wavespeeds for the HLLC Riemann Solver
- Estimating the error of numerical solutions of systems of reaction-diffusion equations
- The dynamical behavior of the discontinuous Galerkin method and related difference schemes
- A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Scalar Convection Diffusion Equations
- Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models
- Invariant Domains and Second-Order Continuous Finite Element Approximation for Scalar Conservation Equations
- Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations
- Algorithms For Positive Polynomial Approximation
- High-Order Bound-Preserving Discontinuous Galerkin Methods for Stiff Multispecies Detonation
- Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
- Asymptotic-Preserving and Positivity-Preserving Implicit-Explicit Schemes for the Stiff BGK Equation
- Discrete maximum principles for nonlinear parabolic PDE systems
- Second-Order Invariant Domain Preserving Approximation of the Euler Equations Using Convex Limiting
- A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics
- Positive schemes and shock modelling for compressible flows
- An invariant‐region‐preserving limiter for DG schemes to isentropic Euler equations
- Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
- Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle
- Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller--Segel and Poisson--Nernst--Planck Equations
- A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
- Minimum Principle on Specific Entropy and High-Order Accurate Invariant-Region-Preserving Numerical Methods for Relativistic Hydrodynamics
- A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving
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