Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus

2019/08/25 by Ting Ma, Ma, Ting, Rongchan Zhu +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1908.09331

openalex publication_date 2019/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on \T. First we prove that the convergence rate for stochastic 2D heat equation is of order α-δ in Besov space \C^-α for α∈(0,1) and δ>0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order α-δ in \C^-α for α∈(0,2/9) and δ>0 arbitrarily small.

Citations

• Space-time approximation of stochastic p-Laplace systems

Cited by

• SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs

Related

• Strong convergence rates for full-discrete approximations of the stochastic Allen-Cahn equations on 2D torus
• Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise
• Weak Convergence Analysis for the Finite Element Approximation to Stochastic Allen-Cahn Equation Driven by Multiplicative White Noise
• Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation
• Weak error analysis for the stochastic Allen-Cahn equation