Unfitted finite element method for the quad-curl interface problem

In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche’s method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure stability, we incorporate ghost penalty terms and a discrete dive...

Full description

Saved in:
Bibliographic Details
Published inAdvances in computational mathematics Vol. 51; no. 1
Main Authors Guo, Hailong, Zhang, Mingyan, Zhang, Qian, Zhang, Zhimin
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.02.2025
Subjects
Divergence
Error analysis
Finite element method
Interface stability
Stiffness matrix
Online AccessGet full text

Cover

More Information
Summary:In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche’s method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure stability, we incorporate ghost penalty terms and a discrete divergence-free term. We establish the well-posedness of our method and demonstrate an optimal error bound in the discrete energy norm. We also analyze the stiffness matrix’s condition number. Our numerical tests back up our theory on convergence rates and condition numbers.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10213-9