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SUMMARY:Adaptive Intrusive Methods for Forward UQ in PDEs - Catherine Powe
 ll (University of Manchester)
DTSTART:20240215T150000Z
DTEND:20240215T160000Z
UID:TALK210127@talks.cam.ac.uk
CONTACT:Nicolas Boulle
DESCRIPTION:In this talk we discuss a so-called intrusive approach for the
  forward propagation of uncertainty in PDEs with uncertain coefficients. S
 pecifically\, we focus on stochastic Galerkin finite element methods (SGFE
 Ms). Multilevel variants of such methods provide polynomial-based surrogat
 es with spatial coefficients that reside in potentially different finite e
 lement spaces. For elliptic PDEs with diffusion coefficients represented a
 s affine functions of countably infinitely many parameters\, well establis
 hed theoretical results state that such methods can achieve rates of conve
 rgence independent of the number of input parameters\, thereby breaking th
 e curse of dimensionality. Moreover\, for nice enough test problems\, it i
 s even possible to prove convergence rates afforded to the chosen finite e
 lement method for the associated deterministic PDE.  However\, achieving t
 hese rates in practice using automated computational algorithms remains hi
 ghly challenging\, and non-intrusive multilevel sampling methods are often
  preferred for their ease of use. We discuss an adaptive framework that is
  driven by a classical hierarchical a posteriori error estimation strategy
  — modified for the more challenging parametric PDE setting — and pres
 ent numerical results.
LOCATION:Centre for Mathematical Sciences\, MR14
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