Legendre spectral element and backward Euler methods for solving a family of stochastic partial differential equations

Mahmoud Lotfi

Legendre spectral element and backward Euler methods for solving a family of stochastic partial differential equations

محل انتشار: دو فصلنامه آنالیز ریاضی و بهینه سازی محدب، دوره: 3، شماره: 2

سال انتشار: 1402

نوع سند: مقاله ژورنالی

زبان: انگلیسی

مشاهده: 32

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https://civilica.com/doc/1900564

شناسه ملی سند علمی:

JR_MACO-3-2_012

تاریخ نمایه سازی: 14 بهمن 1402

چکیده مقاله:

In this paper, we use the spectral element method for solving the stochastic partial differential equation. For spatial discretization, we use the Legendre spectral element method, and we obtain the semi-discrete form. To solve the problem, we need to obtain the complete discrete form and we use the backward Euler method to this aim. The Weiner process is approximated by Fourier series and we obtain the fully discrete scheme of the problem. Error and convergence analysis are presented and, with a numerical example, we demonstrate the efficiency of the proposed method.

کلیدواژه ها:

Stochastic partial differential equation ، spectral element method ، Legendre polynomials

نویسندگان

Mahmoud Lotfi

Farhangian University

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G.Da. Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge ...
L. Gawarecki, V. Mandrekar, Stochastic Differential Equations in Infinite Dimensions ...
W. Grecksch, C. Tudor, Stochastic Evolution Equations. A Hilbert Space ...
C. Prevot, M. Rockner, A Concise Course on Stochastic Partial ...
Y. Cao, L. Yin, Spectral Galerkin method for stochastic wave ...
Y. Cao, L. Yin, Spectral method for nonlinear stochastic partial ...
D. Liu, Convergence of the spectral method for stochastic GinzburgLandau ...
M. Dehghan, M. Shirzadi, Meshless simulation of stochastic advection-diffusion equations ...
M. Dehghan, M. Shirzadi, Numerical solution of stochastic elliptic partial ...
M. Kamrani, Numerical solution of stochastic partial differential equations using ...
M. Kamrani and S.M. Hosseini, Spectral collocation method for stochastic ...
E.J. Allen, S.J. Novosel, Z. Zhang, Finite element and difference ...
I. Babuska, R. Tempone, G.E. Zouraris, Galerkin finite element approximations ...
A. Barth, A. Lang, S imulation of stochastic partial differential ...
F.E. Benth, J. Gjerde, Convergence rates for finite element approximations ...
Y. Cao, Z. Chen, M. Gunzburger, Error analysis of finite ...
A. Jentzen, A.P. Pusnik, Strong convergence rates for an explicit ...
M. Hutzenthaler, A. Jentzen, P.E. Kloeden, Strong convergence of an ...
A. Jentzen, Pathwise numerical approximations of SPDEs with additive noise ...
C. Jianbo, H. Jialin, S. Liying, Weak convergence and invariant ...
R. Courant, Variational method for the solution of problems of ...
A.T. Patera, A spectral element method for fluid dynamics: laminar ...
Y. Maday, A.T. Patera, Spectral Element Methods for the Incompressible ...
K.J. Bathe, Finite Element Procedures, second ed., Prentice-Hall, Englewood Cliffs, ...
E. Priolo and G.A. Seriani, A numerical investigation of Chebyshev ...
Y. Chen, N. Yi, W. Liu, ۷۲۴-۷۲۷ A Legendre–galerkin spectral ...
F. Zeng, H. Ma, T. Zhao, Alternating direction implicit Legendre ...
F.X. Giraldo, Strong and weak Lagrange-Galerkin spectral element methods for ...
E. Zampieri, L.F. Pavarino, Approximation of acoustic waves by explicit ...
R.G. VanO, T.N. Phillips, The choice of spectral element basis ...
C. Xu, Y. Maday, A spectral element method for the ...
Q. Zhuang and L. Chen, Legendre–Galerkin spectral-element method for the ...
A. Khan, C.S. Upadhyay, M. Gerritsma, Spectral element method for ...
Q. Ai, H.Y. Li, Z.Q. Wang, Diagonalized Legendre spectral methods ...
Y. Wang, G. Qin, Z.Q. Wang, An improved time-splitting method ...
M. Lotfi, A. Alipanah, Legendre spectral element method for solving ...
C. Pozrikidis, Introduction to Finite and Spectral Element Methods Using ...
J.S. Hesthaven, S. Gottlieb, D. Gottlieb, Spectral Method for Time-Dependent ...
A. Ern, J.L. Guermond, Theory and Practice of Finite Elements, ...
L.N. Hand, J.D. Finch, Analytical Mechanics, Cambridge University Press, ۲۰۰۸ ...
C. Bernardi, Y. Maday, Approximations Spectrales de Problèmes aux Limites ...
Y. Yan, Galerkin Finite Element Methods for Stochastic Parabolic Partial ...
C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods ...
Z. Zhang, G. E. Karniadakis, Numerical Methods for Stochastic Partial ...
Q. Du, T. Zhang, Numerical approximation of some linear stochastic ...

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