Approximations to the Stochastic Burgers Equation
arXiv:1005.4438 · doi:10.1007/s00332-011-9104-3
Abstract
This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in space and in time. We demonstrate that in this case, different finite difference schemes converge to different limiting processes as the mesh size tends to zero. A theoretical explanation of this phenomenon is given and we formulate a number of conjectures for more general classes of equations, supported by numerical evidence.
Cited by in corpus (20)
- A theory of regularity structures
- Galerkin approximations for the stochastic Burgers equation
- Temporal Integrators for Fluctuating Hydrodynamics
- Rough Burgers-like equations with multiplicative noise
- Instability, rupture and fluctuations in thin liquid films: Theory and computations
- A spatial version of the Itô-Stratonovich correction
- Approximating rough stochastic PDEs
- Exponential moments for numerical approximations of stochastic partial differential equations
- The derivative of the Kardar-Parisi-Zhang equation is not in the KPZ universality class
- Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
- Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise
- Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing
- Approximating three-dimensional magnetohydrodynamics system forced by space-time white noise
- Iterative and Non-iterative Splitting approach of a stochastic Burgers' equation
- Regularity of the solutions to SPDEs in metric measure spaces
- Finite-Volume approximation of the invariant measure of a viscous stochastic scalar conservation law
- Stochastic Burgers-Huxley Equations: Global Solvability, Large Deviations and Ergodicity
- Strong solution of the stochastic Burgers equation
- Universality in driven systems with a multiply-degenerate umbilic point
- Stochastic partial differential equations driven by space-time fractional noises