Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem

DOI10.4171/IFB/154zbMath1129.35088arXiv1111.6312WikidataQ60149125 ScholiaQ60149125MaRDI QIDQ2372145

Omar Lakkis, Markos A. Katsoulakis, Georgios T. Kossioris

Publication date: 24 July 2007

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.6312

zbMATH Keywords

implicit Euler schemenoise regularizationAllen-Cahn problem

Mathematics Subject Classification ID

Monte Carlo methods (65C05) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items

Strong and weak convergence order of finite element methods for stochastic PDEs with spatial white noise, A fully discrete mixed finite element method for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise, Finite Element Methods for the Stochastic Allen--Cahn Equation with Gradient-type Multiplicative Noise, The numerical approximation of stochastic partial differential equations, On the short time asymptotic of the stochastic Allen-Cahn equation, A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a \(\mathcal{C}^2\) boundary, Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations, Fourier spectral methods for some linear stochastic space-fractional partial differential equations, Numerical multi-scaling method to solve the linear stochastic partial differential equations, A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations, Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise, A modified semi-implicit Euler-Maruyama scheme for finite element discretization of SPDEs with additive noise, A Milstein scheme for SPDEs

Cites Work

• Unnamed Item
• Nonlinear parabolic stochastic differential equations with additive colored noise on \({\mathbb{R}}^ d\times {\mathbb{R}}_ +:\) A regulated stochastic quantization
• Brownian fluctuations of the interface in the \(D=1\) Ginzburg-Landau equation with noise
• Large fluctuations for a nonlinear heat equation with noise
• Spectrum for the allen-chan, chan-hillard, and phase-field equations for generic interfaces
• Finite element and difference approximation of some linear stochastic partial differential equations
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• Stochastic Spatial Models
• Numerical Approximation of Some Linear Stochastic Partial Differential Equations Driven by Special Additive Noises
• Dynamical Fluctuations at the Critical Point: Convergence to a Nonlinear Stochastic PDE
• Stochastic Equations in Infinite Dimensions