NDLI: Strong convergence of the finite element method with truncated noise for semilinear parabolic stochastic equations with additive noise

Content Provider	Springer Nature Link
Author	Lindgren, Fredrik Larsson, Stig Kovács, Mihály
Copyright Year	2009
Abstract	We consider a semilinear parabolic PDE driven by additive noise. The equation is discretized in space by a standard piecewise linear finite element method. We show that the orthogonal expansion of the finite-dimensional Wiener process, that appears in the discretized problem, can be truncated severely without losing the asymptotic order of the method, provided that the kernel of the covariance operator of the Wiener process is smooth enough. For example, if the covariance operator is given by the Gauss kernel, then the number of terms to be kept is the quasi-logarithm of the number of terms in the original expansion. Then one can reduce the size of the corresponding linear algebra problem enormously and hence reduce the computational complexity, which is a key issue when stochastic problems are simulated.
Ending Page	320
Page Count	12
Starting Page	309
File Format	PDF
ISSN	10171398
e-ISSN	15729265
Journal	Numerical Algorithms
Issue Number	2-3
Volume Number	53
Language	English
Publisher	Springer US
Publisher Date	2009-03-13
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic partial differential equations Numeric Computing Wiener process Stochastic partial differential equation Theory of Computation Mathematics Semilinear parabolic equation Truncation Algebra Algorithms Error estimate Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Computational methods for stochastic equations Partial differential equations with randomness, stochastic partial differential equations Finite element
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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