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Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He
Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He
Mathematics and Statistics Faculty Research & Creative Works
In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs.
The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent …