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Numerical approximation of time-fractional stochastic Cahn-Hilliard equation with additive fractionally integrated noise

Paper Authors:

Mariam Al-Maskari,

Samir Karaa

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Key Details

Considers time-fractional stochastic Cahn-Hilliard equation with fractionally integrated noise

Proposes and analyzes finite element and convolution quadrature numerical method

Obtains strong convergence rates using energy arguments and Holder continuity

Overcomes analytical challenges from unbounded operator and nonlinearity

Presents supporting numerical experiments

AI generated summary

Numerical approximation of time-fractional stochastic Cahn-Hilliard equation with additive fractionally integrated noise

This paper analyzes numerical methods for approximating solutions to a stochastic, time-fractional Cahn-Hilliard equation with additive, fractionally integrated noise. Key contributions include deriving strong convergence rates for a finite element spatial discretization and convolution quadrature time discretization by using energy arguments. The analysis handles challenges from the unbounded elliptic operator and establishes temporal Holder continuity of the solution. Numerical results validate the convergence rate theory.

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