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DTSTART;TZID=Europe/Paris:20260611T140000
DTEND;TZID=Europe/Paris:20260611T150000
DTSTAMP:20260619T142224
CREATED:20260203T195417Z
LAST-MODIFIED:20260612T073052Z
UID:14755-1781186400-1781190000@lmv.math.cnrs.fr
SUMMARY:EDP : Alexandre Ern (CERMICS\, ENPC) : Implicit-explicit schemes with SUPG stabilization for transient linear transport with diffusion
DESCRIPTION:We analyze Runge–Kutta (RK) implicit-explicit (IMEX) time-stepping schemes to approximate the Cauchy problem associated with a partial differential equation of convection-diffusion-type\, i.e.\, comprising a first-order part (the transport operator) and a second-order part (the diffusion operator). The proposed approach departs from the traditional method of lines\, as the transport part is discretized in space using continuous finite elements with streamline upwind Petrov–Galerkin (SUPG) stabilization\, whereas the diffusion part is discretized using the plain Galerkin method. Contraction in a suitable norm composed of the L^2-norm augmented with a term accounting for the SUPG stabilization is proved for the first-order Lie splitting scheme\, the second-order Strang splitting scheme\, and two third-order Runge–Kutta IMEX methods. All these results require that the coefficient weighting the SUPG stabilization and the Courant number are small enough\, uniformly with respect to the local Peclet number. The contraction property of the third-order IMEX methods also assumes that the discrete diffusion and transport operators commute. This is joint work with Jean-Luc Guermond (Texas A&M).
URL:https://lmv.math.cnrs.fr/evenenement/edp-alexandre-ern-cermics-enpc/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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DTSTART;TZID=Europe/Paris:20260611T151500
DTEND;TZID=Europe/Paris:20260611T160000
DTSTAMP:20260619T142224
CREATED:20260603T094252Z
LAST-MODIFIED:20260612T073058Z
UID:15064-1781190900-1781193600@lmv.math.cnrs.fr
SUMMARY:EDP : Nailya Manatova (LMV) : Infinite point blow-up of the mass critical gKdV
DESCRIPTION:For the L2-critical generalized KdV equation\, blow-up is not possible for subcritical mass elements. A minimal mass blow-up exists\, as does a description of the flow for slightly supercritical mass elements. For such initial data\, a finite-time blow-up occurs with \n\( \|u_x\|_{L^2}\sim(T-t)^{-\nu} \) \nwhere \( \nu \) is the blow-up rate. We will focus on results concerning finite-time infinite-point blow-up\, which occurs for \( \nu \geq 1/2 \). Previously\, the blow-up rate of such solutions was limited with a lower bound of 11/13; in my previous work\, this has been improved to 1/2 strictly.\nThis year I’ve constructed solutions with the blow up rate of 1/2. This rate is in the transition between infinite and finite point blow up\, and corresponds to slow blow up. We will discuss the construction of such solutions and their instability.
URL:https://lmv.math.cnrs.fr/evenenement/edp-nailya-manatova-lmv-finite-point-blow-up-of-the-mass-critical-gkdv/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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