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.
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Communicated by Anders Szepessy.
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.
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Geissert, M., Kovács, M. & Larsson, S. Rate of weak convergence of the finite element method for the stochastic heat equation with additive noise. Bit Numer Math 49, 343–356 (2009). https://doi.org/10.1007/s10543-009-0227-y
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DOI: https://doi.org/10.1007/s10543-009-0227-y
Keywords
- Finite element
- Parabolic equation
- Stochastic
- Additive noise
- Wiener process
- Error estimate
- Weak convergence