Quadratic immersed finite element spaces and their approximation capabilities

Brian Camp, Tao Lin, Yanping Lin, Weiwei Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

33 Citations (Scopus)

Abstract

This paper discusses a class of quadratic immersed finite element (IFE) spaces developed for solving second order elliptic interface problems. Unlike the linear IFE basis functions, the quadratic IFE local nodal basis functions cannot be uniquely defined by nodal values and interface jump conditions. Three types of one dimensional quadratic IFE basis functions are presented together with their extensions for forming the two dimensional IFE spaces based on rectangular partitions. Approximation capabilities of these IFE spaces are discussed. Finite element solutions based on these IFE for representative interface problems are presented to further illustrate capabilities of these IFE spaces.
Original languageEnglish
Pages (from-to)81-112
Number of pages32
JournalAdvances in Computational Mathematics
Volume24
Issue number1-4
DOIs
Publication statusPublished - 1 Jan 2006
Externally publishedYes

Keywords

  • Discontinuous coefficients
  • Error bounds
  • Interface problem
  • Order of convergence
  • Quadratic immersed finite element methods
  • Structured mesh

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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