Geodesic
Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 2, pp. 289-322

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We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method based on C0 or C1 piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates for the modelling error and for the approximation error to the solution of the regularized problem.

DOI : 10.1051/m2an/2010003
Classification : 65M60, 65M15, 65C20
Keywords: finite element method, space-time white noise, backward Euler time-stepping, fully-discrete approximations, a priori error estimates 
@article{M2AN_2010__44_2_289_0,
     author = {Kossioris, Georgios T. and Zouraris, Georgios E.},
     title = {Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {289--322},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {2},
     year = {2010},
     doi = {10.1051/m2an/2010003},
     mrnumber = {2655951},
     zbl = {1189.65018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010003/}
}
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Kossioris, Georgios T.; Zouraris, Georgios E. Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 2, pp. 289-322. doi: 10.1051/m2an/2010003

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