TY  - JOUR
A1  - Höllbacher, Susanne
A1  - Wittum, Gabriel
T1  - A sharp interface method using enriched finite elements for elliptic interface problems
T2  - Numerische Mathematik
N2  - We present an immersed boundary method for the solution of elliptic interface problems with discontinuous coefficients which provides a second-order approximation of the solution. The proposed method can be categorised as an extended or enriched finite element method. In contrast to other extended FEM approaches, the new shape functions get projected in order to satisfy the Kronecker-delta property with respect to the interface. The resulting combination of projection and restriction was already derived in Höllbacher and Wittum (TBA, 2019a) for application to particulate flows. The crucial benefits are the preservation of the symmetry and positive definiteness of the continuous bilinear operator. Besides, no additional stabilisation terms are necessary. Furthermore, since our enrichment can be interpreted as adaptive mesh refinement, the standard integration schemes can be applied on the cut elements. Finally, small cut elements do not impair the condition of the scheme and we propose a simple procedure to ensure good conditioning independent of the location of the interface. The stability and convergence of the solution will be proven and the numerical tests demonstrate optimal order of convergence.
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63684
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-636845
SN  - 0945-3245
N1  - Open Access funding enabled and organized by Projekt DEAL.
VL  - 147
IS  - 4
SP  - 759
EP  - 781
PB  - Springer
CY  - Berlin ; Heidelberg
ER  -