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- W2341969462 abstract "We study finite element approximations for boundary value problems of elliptic semilinear stochastic partial differential equations (SPDEs) driven by Gaussian noises. Formulated in the form of Karhunen-Lo`{e}ve (K-L) expansions, the noises cover some of the most commonly used special cases in physics and engineering applications, including white noises and colored noises characterized by the power-law in non-rectangular domains. Through the convergence analysis for a sequence of approximate solutions of SPDEs where the noises are the truncations of the K-L expansions, we obtain covariance operator dependent sufficient and necessary conditions for the well-posedness of the continuous problem. These SPDEs with truncated noises are then used to construct finite element approximations. A general framework of rigorous error estimates for the finite element approximations is established for the Gaussian noises in the abstract K-L expansion forms. Based on this general framework and with the help of Weyl's law, we derive optimal error estimates for finite element approximations of SPDEs driven by white noises and power-law noises. The error analysis illustrates the effect of the coefficients of the K-L expansions on the overall optimal error estimate of the finite element approximation." @default.
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- W2341969462 date "2015-10-07" @default.
- W2341969462 modified "2023-09-27" @default.
- W2341969462 title "Finite Element Approximations for Semilinear Elliptic Stochastic Partial Differential Equations with Additive Gaussian Noises" @default.
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