„… 72 Chapter 4 Local enrichment of the FCM In the field of numerical analysis, there are several …” „… of order p. As can be seen, in contrast to the problem with no material 74 4 Local enrichment of the …” „… functions of higher order. The local enrichment can be obtained in different ways – such as an h-refinement …”

„… – Heterogeneous materials – Adaptive integration – Moment fitting – Local enrichment – Partition of unity method …” „… . . . . . . . . . . . . . . . . . . . . . . . 69 4 Local enrichment of the FCM 72 4.1 FCM for problems with material interfaces …” „… functions . . . . . . . . . . . . . . . . . . . . . . . 82 4.4 Local enrichment with the aid of the PU …”

„… work was to improve this method from the viewpoint of numerical integration and the local enrichment …” „… . • Local enrichment of the FCM: In order to account for weak discontinuities at material interfaces, we …” „… introduced local enrichment procedure is based on either the hp-d method, the partition of unity method, or a …”

„… integration method. In Chapter 4, we will study the local enrichment of the FCM, which might be needed in the …” „… FCM in simulations of problems including material interfaces, showing that the local enrichment is …” „… able to ensure a high convergence rate for the FCM. The main idea of the proposed local enrichment …”

„… materials. Computational Mechanics, 54:661–675, 2014. [98] M. Joulaian and A. Düster. Local enrichment of …” „… , 2013. [99] M. Joulaian and A. Düster. The hp-d version of the finite cell method with local enrichment …” „… , 1989. [52] K. Dréau, N. Chevaugeon, and N. Moës. Studied X-FEM enrichment to handle material interfaces …”

„… Wiley, 2007, Koutsou et al., 2004). Concentration polarization denotes the local enrichment or depletion …” „… of solutes adjacent to the membranes. A local enrichment arises in the concentrate ow channels …” „… spacers is the separation of adjacent membranes. However, the spacer geometry also governs the local …”

„… , 2014.[93] M. Joulaian and A. Düster. Local enrichment of the finite cell method for problemswith material …” „… cell method formulti-material problems including local enrichment of the ansatz space. Computa-tional …” „… , 392:114648, 2022.[39] J. Dolbow, N. Moës, and T. Belytschko. Discontinuous enrichment in finite elementswith …”

„… Black [10], as well as Dolbow et al. [39]. XFEM considers weakand strong discontinuities via a local …” „… enrichment based on the partition of unity principle.The works of Peskin’s [129], and Haeri and Shrimpton’s …” „… , the FCM would need then to be extended byemploying enrichment procedures, as proposed by [65, 66, 93 …”

„… , B.Sc. Christoph Schäfer, Adam Opel GmbH, Rüsselsheim Abstract To measure system states and local …” „… states and local environmental views can also be achieved using data fusion techniques and digital maps …” „… robust odometry local environmental views can be associated and fused. Furthermore our robust odometry …”

„… . Local enrichment of the finite cell method for problems with material interfaces. Computational …” „… local enrichment for multiscale problems. In Proceedings in Applied Mathematics and Mechanics, volume 13 …” „… high-order enrichment strategy for the finite cell method. Proceedings in Applied Mathematics and Mechanics …”

„… not improve the convergence behavior. Consequently, appropriate enrichment and refinement strategies …” „… to the new one, we present a local radial basis function interpolation scheme. The performance of the …” „… . The remeshing procedure is completed by introducing a local radial basis function interpolation scheme …”

„… performed on cell level manipulating the local stiffness matrix of cut cells. In order to avoid modifying …” „… as a local preconditioning approach. Further, the preconditioner is complemented by an optional …” „… method (SGFEM) – for the one-dimensional case. This stabilization approach is based on a simple local …”