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SUMMARY:A priori and a posteriori error analysis in H(curl): localization\
 , minimal regularity\, and p-optimality
DTSTART:20220927T160000
DTEND:20220927T170000
DTSTAMP:20260406T020624Z
UID:ba3684197513bfc343c0c1bc40bb151fc6bea3427a899b062691bcbb
CATEGORIES:Conferences - Seminars
DESCRIPTION:Martin Vohralík (INRIA)\nWe design a stable local commuting p
 rojector from the entire infinite-dimensional Sobolev space H(curl) onto i
 ts finite-dimensional subspace formed by the Nédélec piecewise polynomia
 ls on a tetrahedral mesh. The projector is defined by simple piecewise pol
 ynomial projections and is stable in the L2 norm\, up to data oscillation.
  It in particular allows to establish the equivalence of local-best and gl
 obal-best approximations in H(curl). This in turn yields to a priori error
  estimates under minimal Sobolev regularity in H(curl)\, localized element
 wise\, optimal both in the mesh size h and in the polynomial degree p. In 
 the heart of the projector\, there is an H(curl)-conforming flux reconstru
 ction procedure. This itself leads to guaranteed\, fully computable\, cons
 tant-free\, and p-robust a posteriori error estimates in H(curl). Details 
 can be found in [1−3].\n\n[1] Chaumont-Frelet\, Théophile and Vohralík
 \, Martin. Equivalence of local-best and global-best approximations in H(c
 url). Calcolo 58 (2021)\, 53.\n[2] Chaumont-Frelet\, Théophile and Vohral
 ík\, Martin. p-robust equilibrated flux reconstruction in H(curl) based o
 n local minimizations. Application to a posteriori analysis of the curl−
 curl problem. HAL Preprint 03227570\, submitted for publication\, 2022.\n[
 3] Chaumont-Frelet\, Théophile and Vohralík\, Martin. A stable local com
 muting projector and optimal hp approximation estimates in H(curl). In pre
 paration\, 2022.
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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