SUMMARY Efficient preconditioning for Oseen‐type problems is an active research topic. We present a novel approach leveraging stabilization for inf‐sup stable discretizations. The Grad‐Div stabilization shares the algebraic properties with an augmented Lagrangian‐type term. Both simplify the approximation of the Schur complement, especially in the convection‐dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov‐type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. Copyright © 2012 John Wiley & Sons, Ltd.

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Titanium was laser nitrided by means of free electron laser (FEL) irradiation in pure nitrogen atmosphere. The variation of macropulse frequency and duration of the FEL micropulse trains resulted in the formation of δ-TiN x coatings with different thicknesses and different micro-and macroscopic morphologies. The coatings revealed characteristic values for hardness, roughness and crystallographic texture, which originate from the growth mechanism, the solid-liquid interface energy and the strain. Further investigations showed that the dendritic growth begins at the surface and the alignment of the dendrites is normal to the surface. A correlation of the texture with the time structure of the laser pulses was found. Combined numerical simulations of temperature evolution and nitrogen diffusion were performed and the results were compared with the experimental findings. The simulations can explain the experimental results to a great extent.

In many numerical schemes for standard turbulence models for the nonstationary, incompressible Navier–Stokes equations, the problem is split into linearized auxiliary problems of advection-diffusion-reaction and of Oseen type. Here we present the numerical analysis of a conforming hp-version for stabilized Galerkin methods of SUPG/PSPG-type of the latter problem whereas the analysis of the former problem is reviewed in Ref. 22. We prove a modified inf–sup condition with a constant, which is independent of the spectral order and the viscosity. Moreover, the analysis of the stabilization parameters highlights the role of grad-div stabilization, in particular in case of div-stable velocity-pressure approximation.

Pure titanium was treated by free electron laser (FEL) radiation in a nitrogen atmosphere. As a result, nitrogen diffusion occurs and a TiN coating was synthesized. Local gradients of interfacial tension due to the local heating lead to a Marangoni convection, which determines the track properties. Because of the experimental inaccessibility of time-dependent occurrences, finite element calculations were performed, to determine the physical processes such as heat transfer, melt flow, and mass transport. In order to calculate the surface deformation of the gasliquid interface, the level set approach was used. The equations were modified and coupled with heat-transfer and diffusion equations. The process was characterized by dimensionless numbers such as the Reynolds, Peclet, and capillary numbers, to obtain more information about the acting forces and the coating development. Moreover, the nitrogen distribution was calculated using the corresponding transport equation. The simulations were compared with crosssectional micrographs of the treated titanium sheets and checked for their validity. Finally, the process presented is discussed and compared with similar laser treatments.