Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations

DOI10.1112/S146115700000125XzbMath1109.37044arXivmath/0506533OpenAlexW2062904358MaRDI QIDQ3430826

Anthony Roberts

Publication date: 4 April 2007

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

Full work available at URL: https://arxiv.org/abs/math/0506533

zbMATH Keywords

finite elementcentre manifold theorydiscretisationsnoisy partial differential equations

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Generation, random and stochastic difference and differential equations (37H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (6)

Centre manifolds for stochastic evolution equations ⋮ COUPLE MICROSCALE PERIODIC PATCHES TO SIMULATE MACROSCALE EMERGENT DYNAMICS ⋮ Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations ⋮ Approximation of the random inertial manifold of singularly perturbed stochastic wave equations ⋮ Centre manifolds for infinite dimensional random dynamical systems ⋮ Averaging approximation to singularly perturbed nonlinear stochastic wave equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcations in fluctuating systems: The center-manifold approach
• A stochastic version of center manifold theory
• Method of stochastic normal forms
• Low-dimensional modelling of dynamics via computer algebra
• Robust algorithms for solving stochastic partial differential equations
• Center manifolds for infinite dimensional nonautonomous differential equations
• Invariant manifolds for stochastic partial differential equations.
• A center-stable manifold theorem for differential equations in Banach spaces
• Geometric singular perturbation theory for stochastic differential equations.
• Modulation equations: Stochastic bifurcation in large domains
• Stochastic modelling: replacing fast degrees of freedom by noise
• TOWARD AN UNDERSTANDING OF STOCHASTIC HOPF BIFURCATION
• A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold
• The application of centre-manifold theory to the evolution of system which vary slowly in space
• Time-discretised Galerkin approximations of parabolic stochastic PDE's
• The asymptotic completeness of inertial manifolds
• A stochastic pitchfork bifurcation in a reaction-diffusion equation
• A holistic finite difference approach models linear dynamics consistently
• Stochastic inertial manifold
• The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipe
• Holistic discretization ensures fidelity to Burgers' equation
• Holistic projection of initial conditions onto a finite difference approximation

This page was built for publication: Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations