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Toward genuinely high order embedded computations: a P1 Shifted Boundary Method with high order fluxes for Darcy problems

Abstract : In this paper, we propose to extend the recent embedded boundary method known as "shifted boundary method" to the Darcy flow problems. The aim is to provide an improved formulation that would give, using linear approximation, at least second order accuracy on bothflux and pressure variables, for any kind of boundary condition, considering embedded simulations.The strategy adopted here is to enrich the approximation of the pressure using Taylor expansions along the edges. The objective of this enrichment is to give a quadratic shape to the pressure. The resulted scheme provides high order accuracy on both variables for embedded simulations with an overall second order accuracy, that is bumped to third order for the pressure when only Dirichletboundaries are embedded.
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https://hal.inria.fr/hal-01877637
Contributor : Mario Ricchiuto <>
Submitted on : Thursday, September 20, 2018 - 10:33:06 AM
Last modification on : Tuesday, August 20, 2019 - 5:12:02 PM
Long-term archiving on: : Friday, December 21, 2018 - 1:41:03 PM

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Léo Nouveau, Mario Ricchiuto, Guglielmo Scovazzi. Toward genuinely high order embedded computations: a P1 Shifted Boundary Method with high order fluxes for Darcy problems. [Research Report] RR-9204, Inria Bordeaux Sud-Ouest. 2018. ⟨hal-01877637⟩

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