A numerical scheme for a class of sweeping processes

DOI10.1007/s00211-010-0329-0zbMath1222.65064arXiv0904.2694OpenAlexW1965328717MaRDI QIDQ543345

Juliette Venel

Publication date: 17 June 2011

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.2694

zbMATH Keywords

algorithmconvergencenumerical examplesdifferential inclusionpredictor-corrector methodcrowd motionsweeping processforward Euler type approximation

Mathematics Subject Classification ID

Ordinary differential inclusions (34A60) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (21)

Nonconvex Integro-Differential Sweeping Process with Applications ⋮ History-dependent operators and prox-regular sweeping processes ⋮ Prox-regularity approach to generalized equations and image projection ⋮ Prox-regular sets and Legendre-Fenchel transform related to separation properties ⋮ Distance function associated to a prox-regular set ⋮ Convex and nonconvex sweeping processes with velocity constraints: well-posedness and insights ⋮ Continuity of the non-convex play operator in the space of rectifiable curves. ⋮ A nonsmooth maximum principle for a controlled nonconvex sweeping process ⋮ On optimal control of a sweeping process coupled with an ordinary differential equation ⋮ Optimality conditions for a controlled sweeping process with applications to the crowd motion model ⋮ Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme ⋮ Existence of solutions for second-order differential inclusions involving proximal normal cones ⋮ Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization ⋮ Optimal control of differential inclusions. II: Sweeping ⋮ Crowd motion from the granular standpoint ⋮ Existence and Lyapunov pairs for the perturbed sweeping process governed by a fixed set ⋮ Convergence of a Particle Method for Diffusive Gradient Flows in One Dimension ⋮ Non-convex sweeping processes in the space of regulated functions ⋮ Nonlocal-interaction equations on uniformly prox-regular sets ⋮ A maximum principle for a time-optimal bilevel sweeping control problem ⋮ Sweeping process by prox-regular sets in Riemannian Hilbert manifolds

Cites Work

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• A mathematical framework for a crowd motion model
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• Relaxation of an optimal control problem involving a perturbed sweeping process
• A discrete contact model for crowd motion
• Local differentiability of distance functions
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• Handling of Contacts in Crowd Motion Simulations
• On various notions of regularity of sets in nonsmooth analysis

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