
Optimal strong convergence rates of some Eulertype timestepping schemes for the finite element discretization SPDEs driven by additive fractional Brownian motion and Poisson r
In this paper, we study the numerical approximation of a general second ...
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Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise
We consider the numerical approximation of the mild solution to a semili...
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Strong convergence of some Eulertype schemes for the finite element discretization of timefractional SPDE driven by standard and fractional Brownian motion
In this work, we provide the first strong convergence result of numerica...
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Error estimates of the backward EulerMaruyama method for multivalued stochastic differential equations
In this paper, we derive error estimates of the backward EulerMaruyama ...
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A linear implicit Euler method for the finite element discretization of a controlled stochastic heat equation
We consider a numerical approximation of a linear quadratic control prob...
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L^pConvergence Rate of Backward Euler Schemes for Monotone SDEs
We give a unified method to derive the strong convergence rate of the ba...
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On differentiable local bounds preserving stabilization for Euler equations
This work is focused on the design of nonlinear stabilization techniques...
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Strong convergence of the backward Euler approximation for the finite element discretization of semilinear parabolic SPDEs with nonglobal Lipschitz drift driven by additive no
This paper deals with the backward Euler method applied to semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. The SPDE is discretized in space by the finite element method and in time by the backward Euler. We consider a larger class of nonlinear drift functions, which are of Nemytskii type and polynomial of any odd degree with negative leading term, instead of only dealing with the special case of stochastic AllenChan equation as in the up to date literature.Moreover our linear operator is of second order and not necessarily selfadjoint, therefore makes estimates more challenging than in the case of selfadjoint operator. We prove the strong convergence of our fully discrete schemes toward the mild solution and results indicate how the convergence rates depend on the regularities of the initial data and the noise. In particular, for trace class noise, we achieve convergence order O (h^2+Δ t^1ϵ), where ϵ>0 is positive number, small enough. We also provide numerical experiments to illustrate our theoretical results.
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