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Chou, So-Hsiang; Attanayake, C.

Construction of discontinuous enrichment functions for enriched or generalized FEM’s for interface elliptic problems in 1D. (English) Zbl 07711020

J. Comput. Appl. Math. 428, Article ID 115180, 13 p. (2023).
Summary: We introduce an enriched unfitted finite element method to solve 1D elliptic interface problems with discontinuous solutions, including those having implicit or Robin-type interface jump conditions. We present a novel approach to construct a one-parameter family of discontinuous enrichment functions by finding an optimal order interpolating function to the discontinuous solutions. In the literature, an enrichment function is usually given beforehand, not related to the construction step of an interpolation operator. Furthermore, we recover the well-known continuous enrichment function when the parameter is set to zero. To prove its efficiency, the enriched linear and quadratic elements are applied to a multi-layer wall model for drug-eluting stents in which zero-flux jump conditions and implicit concentration interface conditions are both present.

Cited in 1 Document

MSC:

65Nxx Numerical methods for partial differential equations, boundary value problems
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Jxx Elliptic equations and elliptic systems

Keywords:

enriched finite element; elliptic interface; generalized finite element analysis; implicit interface jump condition; Robin interface jump condition; linear and quadratic finite elements

Software:

IIMPACK
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Full Text: DOI arXiv

References:

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