An implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic Markov processes

DOI10.1016/j.cam.2007.10.053zbMath1158.65008OpenAlexW2013392595MaRDI QIDQ955050

Robert Eymard, Alain Prignet, Sophie Bloch-Mercier

Publication date: 18 November 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.10.053

zbMATH Keywords

convergencenumerical examplesfinite volume schemepiecewise-deterministic Markov processesChapman-Kolmogorov equationsgrowth-collapse Markov processeslinear hyperbolic problems with measure solutionsweak bounded variation inequalities

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Markov renewal processes, semi-Markov processes (60K15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items

Optimal control of a class of piecewise deterministic processes ⋮ Importance and sensitivity analysis in dynamic reliability ⋮ Convergence of implicit Finite Volume methods for scalar conservation laws with discontinuous flux function ⋮ Convergence of a misanthrope process to the entropy solution of 1D problems ⋮ Finite volume schemes for the approximation via characteristics of linear convection equations with irregular data ⋮ A Fokker-Planck control framework for stochastic systems ⋮ Applications of approximate gradient schemes for nonlinear parabolic equations.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear elliptic equations in \(\mathbb{R}^ N\) without growth restrictions on the data
• Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh
• Existence and uniqueness of the entropy solution to a nonlinear hyperbolic equation
• Stochastic algorithms
• Characterization of the marginal distributions of Markov processes used in dynamic reliability
• Discrete Sobolev inequalities andL^perror estimates for finite volume solutions of convection diffusion equations
• A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data
• A Markovian growth-collapse model
• A finite-volume scheme for dynamic reliability models