Strong Convergence of the Finite Element Method for Stochastic Partial Differential Equations with Additive Noise

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Aghaei, Mohammad Reza | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 47776 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohuri Zangeneh, Bijan
Abstract:
We study linear and semilinear stochastic evolution partial differential equations driven by additive noise. We present a general and flexible framework for representing the infinite dimensional Wiener process, which drives the equation. The equation is discretized in space by a standard piecewise linear finite element method. We show how to obtain error estimates when the truncated expansion is used in the equation. We show that the orthogonal expansion of the finite-dimensional Wiener process, that appears in the discretized problem, can be truncated severely without losing theasymptotic order of the method, provided that the kernel of the covariance operator of the Wiener process is smooth enough
Keywords:
Estimation Error ; Finite Element Method ; Wiener Index ; Semi-Linear Parabolic Equation ; Stochastic Partial Differential Equation ; Stochastic Wave