Journal
ADVANCES IN COMPUTATIONAL MATHEMATICS
Volume 24, Issue 1-4, Pages 81-112Publisher
SPRINGER
DOI: 10.1007/s10444-004-4139-8
Keywords
interface problem; discontinuous coefficients; structured mesh; quadratic immersed finite element methods; order of convergence; error bounds
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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.
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