The Influence of Quadrature Errors on Isogeometric Mortar Methods

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant

Methodische und klinische Evaluation einer neuen enzymimmunologischen Methode zur Bestimmung des Thyroxin bindenden Globulins (TBG) und des T4/TBG-Quotienten: Eine multizentrische Studie

Peer Reviewe

A framework for polyconvex large strain phase-field methods to fracture

Variationally consistent phase-field methods have been shown to be able to predict complex three-dimensional crack patterns. However, current computational methodologies in the context of large deformations lack the necessary numerical stability to ensure robustness in different loading scenarios. In this work, we present a novel formulation for finite strain polyconvex elasticity by introducing a new anisotropic split based on the principal invariants of the right Cauchy-Green tensor, which always ensures polyconvexity of the resulting strain energy function. The presented phase-field approach is embedded in a sophisticated isogeometrical framework with hierarchical refinement for three-dimensional problems using a fourth order Cahn-Hilliard crack density functional with higher-order convergence rates for fracture problems. Additionally, we introduce for the first time a Hu-Washizu mixed variational formulation in the context of phase-field problems, which permits the novel introduction of a variationally consistent stress-driven split. The new polyconvex phase-field fracture formulation guarantees numerical stability for the full range of deformations and for arbitrary hyperelastic materials

An energy stable one-field monolithic arbitrary Lagrangian-Eulerian formulation for fluid-structure interaction

In this article we present a one-field monolithic finite element method in the Arbitrary Lagrangian–Eulerian (ALE) formulation for Fluid–Structure Interaction (FSI) problems. The method only solves for one velocity field in the whole FSI domain, and it solves in a monolithic manner so that the fluid solid interface conditions are satisfied automatically. We prove that the proposed scheme is unconditionally stable, through energy analysis, by utilising a conservative formulation and an exact quadrature rule. We implement the algorithm using both F-scheme and D-scheme, and demonstrate that the former has the same formulation in two and three dimensions. Finally several numerical examples are presented to validate this methodology, including combination with remesh techniques to handle the case of very large solid displacement

A theoretical and numerical investigation of a family of immersed finite element methods

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of these methods, based upon an operator splitting scheme, in order to demonstrate that both the explicit IFEM and the one-field FDM can be regarded as particular linearizations of the fully implicit IFEM. However, the one-field FDM can be shown to be more robust than the explicit IFEM and can simulate a wider range of solid parameters with a relatively large time step. In addition, it can produce results almost identical to the implicit IFEM but without iteration inside each time step. We study the effect on these methods of variations in viscosity and density of fluid and solid materials. The advantages of the one-field FDM within the IFEM framework are illustrated through a selection of parameter sets for two benchmark cases