Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus

Ma T, Zhu R (2020)
ACTA MATHEMATICA SINICA-ENGLISH SERIES.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Abstract / Bemerkung
In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on T2. First we prove that the convergence rate for stochastic 2D heat equation is of order a - d in Besov space C-a for a. (0, 1) and d > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order a - d in C- a for a. (0, 2/9) and d > 0 arbitrarily small.
Stichworte
Stochastic Allen-Cahn equations; convergence rate; Galerkin projection; Besov space; white noise
Erscheinungsjahr
2020
Zeitschriftentitel
ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN
1439-8516
eISSN
1439-7617
Page URI
https://pub.uni-bielefeld.de/record/2943301

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Ma T, Zhu R. Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus. ACTA MATHEMATICA SINICA-ENGLISH SERIES. 2020.
Ma, T., & Zhu, R. (2020). Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus. ACTA MATHEMATICA SINICA-ENGLISH SERIES. doi:10.1007/s10114-020-9367-4
Ma, T., and Zhu, R. (2020). Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus. ACTA MATHEMATICA SINICA-ENGLISH SERIES.
Ma, T., & Zhu, R., 2020. Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus. ACTA MATHEMATICA SINICA-ENGLISH SERIES.
T. Ma and R. Zhu, “Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus”, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2020.
Ma, T., Zhu, R.: Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus. ACTA MATHEMATICA SINICA-ENGLISH SERIES. (2020).
Ma, Ting, and Zhu, Rongchan. “Convergence Rate for Galerkin Approximation of the Stochastic Allen-Cahn Equations on 2D Torus”. ACTA MATHEMATICA SINICA-ENGLISH SERIES (2020).