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Rate of weak convergence of the finite element method for the stochastic heat equation with additive noise |
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| Authors: | Matthias Geissert Mihály Kovács Stig Larsson |
| Affiliation: | 1.Technische Universit?t Darmstadt, Fachbereich Mathematik,Darmstadt,Germany;2.Department of Mathematics and Statistics,University of Otago,Dunedin,New Zealand;3.Department of Mathematical Sciences,Chalmers University of Technology and University of Gothenburg,G?teborg,Sweden |
| Abstract: | The stochastic heat equation driven by additive noise is discretized in the spatial variables by a standard finite element method. The weak convergence of the approximate solution is investigated and the rate of weak convergence is found to be twice that of strong convergence. M. Kovács and S. Larsson supported by the Swedish Research Council (VR). Part of this work was done at Institut Mittag-Leffler. S. Larsson supported by the Swedish Foundation for Strategic Research (SSF) through GMMC, the Gothenburg Mathematical Modelling Centre. |
| Keywords: | Finite element Parabolic equation Stochastic Additive noise Wiener process Error estimate Weak convergence |
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