2017
DOI: 10.1007/s10915-017-0475-y
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Strong Convergence Analysis of the Stochastic Exponential Rosenbrock Scheme for the Finite Element Discretization of Semilinear SPDEs Driven by Multiplicative and Additive Noise

Abstract: In this paper, we consider the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear part is stronger than the linear part also called stochastic reactive dominated transport equations. Most numerical techniques, including current stochastic exponential integrators lose their good stability properties on such equations. Using finite element for space discret… Show more

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Cited by 15 publications
(45 citation statements)
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References 33 publications
(95 reference statements)
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“…As in the current literature for deterministic Rosenbrock-type methods, [28,29], deterministic exponential Rosemnbrock-type method [10,27] and stochastic exponential Rosenbrock-type methods [26], we make the following assumption on the nonlinear drift term.…”
Section: Main Assumptions and Well Posedness Problemmentioning
confidence: 99%
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“…As in the current literature for deterministic Rosenbrock-type methods, [28,29], deterministic exponential Rosemnbrock-type method [10,27] and stochastic exponential Rosenbrock-type methods [26], we make the following assumption on the nonlinear drift term.…”
Section: Main Assumptions and Well Posedness Problemmentioning
confidence: 99%
“…To establish our L p strong convergence result when dealing with multiplicative noise, we will also need the following further assumption on the diffusion term when β ∈ [1,2), which was also used in [13,19] to achieve optimal regularity order and in [18,22,26] to achieve optimal convergence order in space and time.…”
Section: Assumption 4 [Diffusion Term ]mentioning
confidence: 99%
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“…When we turn our attention to the case of semilinear SPDEs, still with constant operator A(t) = A, but not necessary self-adjoint, the list of references becomes remarkably short, see e.g. [24,31]. Note that modelling real world phenomena with time dependent linear operator is more realistic than modelling with time independent linear 2 operator (see e.g.[4] and references therein).…”
mentioning
confidence: 99%