Item request has been placed! ×
Item request cannot be made. ×
loading  Processing Request

An analysis of high-frequency Helmholtz problems in domains with conical points and their finite element discretization

Item request has been placed! ×
Item request cannot be made. ×
loading   Processing Request
Read More Add to Saved list
  • Additional Information
    • Contributors:
      Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée (ATLANTIS); Inria Sophia Antipolis - Méditerranée (CRISAM); Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD); Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA); Laboratoire Jean Alexandre Dieudonné (LJAD); Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA); Laboratoire de Matériaux Céramiques et de Mathématiques (CERAMATHS); Université Polytechnique Hauts-de-France (UPHF)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France); Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA); INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France); Institut National des Sciences Appliquées (INSA)
    • Publication Information:
      HAL CCSD
      De Gruyter
    • Publication Date:
      2022
    • Collection:
      Université Polytechnique Hauts-de-France: HAL
    • Abstract:
      International audience ; We consider Helmholtz problems in three-dimensional domains featuring conincal points. We focus on the high-frequency regime and derive novel sharp upper-bounds for the stress intensity factors of the singularities associated with the conical points. We then employ these new estimates to analyse the stability of finite element discretizations. Our key result is that lowest-order Lagrange finite elements are stable under the assumption that "omega^2 h is small". This assumption is standard and well-known in the case of smooth domains, and we show that it naturally extends to domain with conical points, even when using uniform meshes.
    • Relation:
      hal-04001691; https://inria.hal.science/hal-04001691; https://inria.hal.science/hal-04001691/document; https://inria.hal.science/hal-04001691/file/chaumontfrelet_nicaise_2022a.pdf
    • Accession Number:
      10.1515/cmam-2022-0126
    • Online Access:
      https://doi.org/10.1515/cmam-2022-0126
      https://inria.hal.science/hal-04001691
      https://inria.hal.science/hal-04001691/document
      https://inria.hal.science/hal-04001691/file/chaumontfrelet_nicaise_2022a.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.22FEE0DA