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SUMMARY:Numerical solution of partial differential equations with random c
 oefficients: a stochastic finite element approach - Dr Eveline Rosseel\, K
 atholieke Universiteit Leuven
DTSTART:20101126T140000Z
DTEND:20101126T150000Z
UID:TALK25981@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:Mathematical models of engineering systems and physical proces
 ses typically take the form of a partial differential equation (PDE). Vari
 ability or uncertainty on coefficients of a PDE can be expressed by introd
 ucing random variables\, random fields or random processes into the PDE. R
 ecently developed stochastic finite element methods enable the constructio
 n of high-order accurate solutions of a stochastic PDE\, while reducing th
 e high computational cost of more standard uncertainty quantification meth
 ods\, such as the Monte Carlo simulation method.\n\n\nIn this talk\, we ou
 tline the methodology of the two main variants of the stochastic finite el
 ement method\, i.e.\, the stochastic collocation and the stochastic Galerk
 in method. Both methods transform a stochastic PDE into a system of determ
 inistic PDEs. In the latter case\, the number of deterministic PDEs is gen
 erally smaller than for the stochastic collocation method\, but the system
  is more complicated to solve. We will point out how these methods can be 
 applied to efficiently solve a small flow problem through random porous me
 dia. Multigrid techniques lead to a fast solution of the resulting systems
 . These simulations can be extended to solve groundwater flow problems or 
 to perform oil reservoir simulations.
LOCATION:Oatley Seminar Room\, Department of Engineering
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