Nonnegativity preserving convergent schemes for stochastic porous-medium equations

DOI10.1090/mcom/3372zbMath1448.65159OpenAlexW2801453024MaRDI QIDQ4612560

Hubertus Grillmeier, Günther Grün

Publication date: 31 January 2019

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

Full work available at URL: https://doi.org/10.1090/mcom/3372

zbMATH Keywords

martingale solutionstochastic porous-medium equationnonnegativity-preserving schemestochastic free-boundary problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Numerical solutions to stochastic differential and integral equations (65C30) Free boundary problems for PDEs (35R35) Simulation of dynamical systems (37M05) Infinite-dimensional random dynamical systems; stochastic equations (37L55) Positive solutions to PDEs (35B09)

Related Items

Numerical approximation of nonlinear SPDE's ⋮ Existence of Positive Solutions to Stochastic Thin-Film Equations ⋮ On stochastic porous-medium equations with critical-growth conservative multiplicative noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Localization of solutions to stochastic porous media equations: finite speed of propagation
• Stochastic porous media equations and self-organized criticality
• Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval
• Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
• Nonnegativity preserving convergent schemes for the thin film equation
• Strong solutions for stochastic partial differential equations of gradient type
• The Euler scheme with irregular coefficients
• Theory and practice of finite elements.
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Weak convergence and empirical processes. With applications to statistics
• Existence of strong solutions for Itô's stochastic equations via approximations
• Finite time extinction for stochastic sign fast diffusion and self-organized criticality
• Lower bounds on waiting times for degenerate parabolic equations and systems
• Equations stochastiques du type Navier-Stokes
• On the stochastic porous medium equation
• Finite-element-based discretizations of the incompressible Navier-Stokes equations with multiplicative random forcing
• Finite Speed of Propagation for Stochastic Porous Media Equations
• How an Initially Stationary Interface Begins to Move in Porous Medium Flow
• Numerical Methods for Elliptic and Parabolic Partial Differential Equations
• Existence of Positive Solutions to Stochastic Thin-Film Equations
• On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions
• Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
• Stochastic Equations in Infinite Dimensions
• Finite Speed of Propagation and Waiting Times for the Stochastic Porous Medium Equation: A Unifying Approach
• A convergent finite-element-based discretization of the stochastic Landau-Lifshitz-Gilbert equation
• Existence and uniqueness of nonnegative solutions to the stochastic porous media equation