An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II. Piecewise-smooth interfaces

We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the reliable cell merging algorithm for smooth interfaces to automatica...

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Bibliographic Details
Published inApplied numerical mathematics Vol. 206; pp. 247 - 268
Main Authors Chen, Zhiming, Liu, Yong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2024
Subjects
Cell merging
Piecewise-smooth interface
Unfitted finite element method
65N50
Unfitted finite element method
Piecewise-smooth interface
65N30
Cell merging
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ISSN0168-9274
DOI10.1016/j.apnum.2024.08.012

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Summary:We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the reliable cell merging algorithm for smooth interfaces to automatically generate the induced mesh for piecewise smooth interfaces. An hp a posteriori error estimate is derived for a new unfitted finite element method whose finite element functions are conforming in each subdomain. Numerical examples illustrate the competitive performance of the method.
ISSN:0168-9274
DOI:10.1016/j.apnum.2024.08.012