A5090331246- Advanced Numerical Methods in Computational Mathematics
- Advanced Mathematical Modeling in Engineering
- Computational Fluid Dynamics and Aerodynamics
- Fluid Dynamics and Turbulent Flows
- Lattice Boltzmann Simulation Studies
- Solidification and crystal growth phenomena
- Fluid Dynamics and Thin Films
- Fluid Dynamics and Heat Transfer
- Nanofluid Flow and Heat Transfer
- Rheology and Fluid Dynamics Studies
- Numerical methods in engineering
- Advanced Numerical Analysis Techniques
- Numerical methods for differential equations
- Model Reduction and Neural Networks
- Laser Material Processing Techniques
- Spacecraft and Cryogenic Technologies
- Microfluidic and Bio-sensing Technologies
- Topology Optimization in Engineering
- Nonlinear Dynamics and Pattern Formation
- Aluminum Alloy Microstructure Properties
- Ocular and Laser Science Research
- Stability and Controllability of Differential Equations
- Composite Structure Analysis and Optimization
- Fluid Dynamics Simulations and Interactions
- Metallurgical Processes and Thermodynamics
Friedrich-Alexander-Universität Erlangen-Nürnberg
2015-2024
Eberspächer (Germany)
2011
Technische Universität Berlin
2009
Weierstrass Institute for Applied Analysis and Stochastics
2001-2005
Freie Universität Berlin
2002-2004
University of Bremen
1998-2003
University of Freiburg
1991-1998
In this article a boundary feedback stabilization approach for incompressible Navier--Stokes flows is studied. One of the main difficulties encountered fact that after space discretization by mixed finite element method (because solenoidal condition) one ends up with differential algebraic system index 2. The remedy here to use discrete realization Leray projection used Raymond [J.-P. Raymond, SIAM J. Control Optim., 45 (2006), pp. 790--828] analyze and stabilize continuous problem. Using...
We derive residual-based a posteriori error estimates of optimal order for fully discrete approximations linear parabolic problems. The time discretization uses the Crank--Nicolson method, and space finite element spaces that are allowed to change in time. main tool our analysis is comparison with an appropriate reconstruction solution, which introduced present paper.
We present a finite element method for the simulation of all relevant processes evaporation liquid droplet suspended in an acoustic levitation device. The mathematical model and numerical implementation take into account heat mass transfer across interface between gaseous phase influence streaming on this process, as well displacement deformation due to radiation pressure. apply several theoretical experimental examples compare our results with well-known d2-law spherical droplets...
We introduce and study an adaptive finite element method (FEM) for the Stokes system based on Uzawa outer iteration to update pressure elliptic inner velocity. show linear convergence in terms of counter pairs spaces consisting continuous elements degree k velocity, whereas can be either discontinuous k-1 or k. The popular Taylor--Hood family is sole example stable included theory, which turn relies stability problem thus makes no use discrete inf-sup condition. discuss realization...
Surface diffusion is a (fourth-order highly nonlinear) geometric driven motion of surface with normal velocity proportional to the Laplacian mean curvature. We present novel variational formulation for graphs and derive priori error estimates time-continuous finite element discretization. also introduce semi-implicit time discretization Schur complement approach solve resulting fully discrete, linear systems. After computational verification orders convergence polynomial degrees 1 2, we show...
We present the topology optimization of an assembly consisting a piezoelectric layer attached to plate with support. The domain is layer. Using SIMP (Solid Isotropic Material Penalization) method forced vibrations by harmonic electrical excitation, we achieve maximization dynamic displacement. show that considered objective function can be used under certain boundary conditions optimize sound radiation. vibrational patterns resulting from are analysed in comparison modes eigenvalue analysis....
The dendritic growth of crystals under gravity influence shows a strong dependence on convection in the liquid. situation is modelled by Stefan problem with Gibbs-Thomson condition coupled Navier-Stokes equations liquid phase. A finite element method for numerical simulation crystal including effects presented. It consists parametric evolution interface, solvers heat equation and time dependent domain. Results from simulations two space dimensions Dirichlet transparent boundary conditions...
SUMMARY In this article, an ALE finite element method to simulate the partial melting of a workpiece metal is presented. The model includes heat transport in both solid and liquid part, fluid flow phase by Navier–Stokes equations, tracking melt interface solid/liquid Stefan condition, treatment capillary boundary accounting for surface tension effects radiative condition. We show that accurate moving boundaries crucial resolve their respective influences on field thus overall energy...
In this paper, a mathematical model for the dynamics of superparamagnetic iron oxide nanoparticles (SPIONs) in laminar flow through pipe under influence an external magnetic field single electromagnet is derived. The consists convection–diffusion equation coupled with magnetostatic equations. accumulation particles along boundary modeled help surface concentration. Based on experimental data describing retention lauric acid coated SPIONs tubular field, parametrized and finite element...
In this article we study finite element approximations of the time-dependent Stokes system on dynamically changing meshes. Applying backward Euler method for time discretization use discrete Helmholtz or projection to evaluate solution at tn−1 new spatial mesh tn. The theoretical results consist a priori error estimates that show dependence step size not better than 𝒪(1/Δt). These surprisingly pessimistic upper bounds are complemented by numerical examples giving evidence negative...
We consider a finite element discretization by the Taylor–Hood for stationary Stokes and Navier–Stokes equations with slip boundary condition. The condition is enforced pointwise nodal values of velocity in nodes. prove optimal error estimates H1 L2 norms pressure respectively.