Discretization of flux-limited gradient flows: $\Gamma $-convergence and numerical schemes

DOI10.1090/mcom/3492zbMath1437.35423arXiv1910.09843OpenAlexW2979425544MaRDI QIDQ5216722

Daniel Matthes, Benjamin Söllner

Publication date: 18 February 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.09843

zbMATH Keywords

gradient flowspace-time discretizationflux-limited equationJKO minimizers

Mathematics Subject Classification ID

Numerical methods involving duality (49M29) Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (2)

Entropic Regularization of NonGradient Systems ⋮ Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems

Cites Work

• Unnamed Item
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• A convergent Lagrangian discretization for a nonlinear fourth-order equation
• Discretization of functionals involving the Monge-Ampère operator
• Some regularity results on the `relativistic' heat equation
• Constructing a relativistic heat flow by transport time steps
• A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes
• A blob method for diffusion
• The optimal mass transport problem for relativistic costs
• A gradient flow approach to a thin film approximation of the Muskat problem
• The Dirichlet problem associated to the relativistic heat equation
• Convergence of the `relativistic' heat equation to the heat equation as \(c\to\infty\)
• Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• On the relativistic heat equation in one space dimension
• A Fully Discrete Variational Scheme for Solving Nonlinear Fokker--Planck Equations in Multiple Space Dimensions
• Numerical Simulation of Diffusive and Aggregation Phenomena in Nonlinear Continuity Equations by Evolving Diffeomorphisms
• Scaling algorithms for unbalanced optimal transport problems
• Long-time behavior of a finite volume discretization for a fourth order diffusion equation
• Entropic Approximation of Wasserstein Gradient Flows
• Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak–Keller–Segel Model
• Lubrication approximation with prescribed nonzero contact anggle
• The Variational Formulation of the Fokker--Planck Equation
• Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation
• Convergence of Entropic Schemes for Optimal Transport and Gradient Flows

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