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The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions. For the analysis of complex geometries, it circumvents expensive and potentially error-prone meshing procedures, while maintaining high rates of convergence. The present contribution provides an overview of recent accomplishments in the FCM with applications in structural mechanics. First, we review the basic components of the technology using the p- and B-spli
The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation be
Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening the hierarchical models into an equation system for analysis. However, the large-scale eq
In this paper, several projection method based preconditioners for various incompressible flow models are studied. In particular, we are interested in the theoretical analysis of a pressure-correction projection method based preconditioner cite{griff
In this paper, we present a new full-discrete finite element method for the heat equation, and show the numerical stability of the method by verified computations. Since, in the error analysis, we use the constructive error estimates proposed ny Naka
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite element a