Accelerated finite elements schemes for parabolic stochastic partial differential equations

  • István Gyöngy
  • Annie MilletEmail author


For a class of finite elements approximations for linear stochastic parabolic PDEs it is proved that one can accelerate the rate of convergence by Richardson extrapolation. More precisely, by taking appropriate mixtures of finite elements approximations one can accelerate the convergence to any given speed provided the coefficients, the initial and free data are sufficiently smooth.


Stochastic parabolic equations Richardson extrapolation Finite elements 

Mathematics Subject Classification

Primary 60H15 65M60 Secondary 65M15 65B05 



This work started while István Gyöngy was an invited professor at the University Paris 1 Panthéon Sorbonne. It was completed when Annie Millet was invited by the University of Edinburgh. Both authors want to thank the University Paris 1, the Edinburgh Mathematical Society and the Royal Society of Edinburgh for their financial support. The authors want to thank the anonymous referees for their careful reading and helpful remarks.


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Authors and Affiliations

  1. 1.Maxwell Institute and School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.SAMM (EA 4543), Université Paris 1 Panthéon SorbonneParis Cedex 13France
  3. 3.Laboratoire de Probabilités, Statistique et Modélisation (LPSM, UMR 8001)ParisFrance

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