Quadratic immersed finite element spaces and their approximation capabilities

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

41 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)81-112
Journal / PublicationAdvances in Computational Mathematics
Volume24
Issue number1-4
Publication statusPublished - Jan 2006

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. © Springer 2006.

Research Area(s)

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

Citation Format(s)

Quadratic immersed finite element spaces and their approximation capabilities. / Camp, Brian; Lin, Tao; Lin, Yanping et al.
In: Advances in Computational Mathematics, Vol. 24, No. 1-4, 01.2006, p. 81-112.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review