Français
A posteriori error estimates and solver adaptivity in numerical simulations
Multi angle
Authors : Vohralík, Martin (Author of the conference)
CIRM (Publisher )
65N15 - Error bounds (BVP of PDE)
65N22 - Solution of discretized equations (BVP of PDE)
65Y05 - Parallel computation (numerical methods)
CIRM (Publisher )
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Abstract :
We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic solver (conjugate gradients, multigrid, domain decomposition, ...). Identifying the discretization, linearization, and algebraic error components, we design local stopping criteria which keep them in balance. This gives rise to a fully adaptive inexact Newton method. Numerical experiments are presented in confirmation of the theory.
MSC Codes : 65N15 - Error bounds (BVP of PDE)
65N22 - Solution of discretized equations (BVP of PDE)
65Y05 - Parallel computation (numerical methods)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/08/2016 Conference Date : 28/07/2016 Subseries : Research talks arXiv category : Numerical Analysis Mathematical Area(s) : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 01:12:27 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-07-28_Vohralik.mp4 
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Information on the Event
Event Title : CEMRACS: Numerical challenges in parallel scientific computing / CEMRACS : Défis numériques en calcul scientifique parallèleEvent Organizers : Grigori, Laura ; Japhet, Caroline ; Moireau, Philippe ; Parnaudeau, Philippe Dates : 18/07/2016 - 26/08/2016 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1430.html
Citation Data
DOI : 10.24350/CIRM.V.19025603Cite this video as: Vohralík, Martin (2016). A posteriori error estimates and solver adaptivity in numerical simulations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19025603 URI : http://dx.doi.org/10.24350/CIRM.V.19025603 |
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