Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise
Provides rigorous convergence analysis for numerical methods of a class of stochastic PDEs, benefiting researchers in numerical analysis and stochastic modeling.
The paper proves sharp-order convergence (up to a logarithmic factor) of finite element and convolution quadrature approximations for stochastic partial integro-differential equations driven by white noise, supported by numerical examples.
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and convolution quadrature for time discretization. Sharp-order convergence of the numerical solutions is proved up to a logarithmic factor. Numerical examples are provided to support the theoretical analysis.