Quadratic immersed finite element spaces and their approximation capabilities

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. Dedicated to the 60th birthday of Charles A. Micchelli Mathematics subject classifications (2000) 65N15, 65N30, 65N50, 65Z05. Yanping Lin: Supported by NSERC. Weiwei Sun: This work was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project CityU 1141/01P).