Weak convergence for a stochastic exponential integrator and finite element discretization of stochastic partial differential equation with multiplicative \& additive noise

DOI10.1016/j.apnum.2016.04.013zbMath1346.65002arXiv1507.07153OpenAlexW2346456776WikidataQ115360409 ScholiaQ115360409MaRDI QIDQ739016

Jean Medard T. Ngnotchouye, Antoine Tambue

Publication date: 16 August 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.07153

zbMATH Keywords

strong convergenceweak convergenceMalliavin calculusfinite element methodssemidiscretizationnumerical resultexponential integratorsexponential Euler schemesemi-linear stochastic partial differential equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solutions to stochastic differential and integral equations (65C30) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (14)

Stochastic exponential integrators for a finite element discretisation of SPDEs with additive noise ⋮ A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations ⋮ Delay dependent asymptotic mean square stability analysis of the stochastic exponential Euler method ⋮ Strong convergence of a fractional exponential integrator scheme for finite element discretization of time-fractional SPDE driven by fractional and standard Brownian motions ⋮ Weak convergence of the finite element method for semilinear parabolic SPDEs driven by additive noise ⋮ Optimal strong convergence rates of numerical methods for semilinear parabolic SPDE driven by Gaussian noise and Poisson random measure ⋮ Strong convergence analysis of the stochastic exponential Rosenbrock scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise ⋮ Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise ⋮ Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs ⋮ Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient ⋮ A note on exponential Rosenbrock-Euler method for the finite element discretization of a semilinear parabolic partial differential equation ⋮ Optimal strong convergence rates of some Euler-type timestepping schemes for the finite element discretization SPDEs driven by additive fractional Brownian motion and Poisson random measure ⋮ Optimal error estimate of the finite element approximation of second order semilinear non-autonomous parabolic PDEs ⋮ A modified semi-implicit Euler-Maruyama scheme for finite element discretization of SPDEs with additive noise

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