Publications by Lutz Tobiska

Lutz Tobiska - Publications

2012-2017

• M. Krasnyk, M. Mangold, S. Ganesan, L. Tobiska:

Numerical reduction of a crystallizer model with internal and external coordinates by proper orthogonal decomposition

Chemical Engrg. Science 70(2012), 77-86

• D. Juhnke, L. Tobiska:

A local projection type stabilization with exponential enrichments applied to one-dimensional advection-diffusion equationsd

Comp.Math.Appl.Mech.Engrg.201-204(2012), 179-190

•2006-2011

• P. Knobloch, L. Tobiska:

On the stability of finite-element discretizations of convection-diffusion-reaction equations.

IMA J. Numer. Anal. 31(2011), 147-164

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• H. Eichel, L. Tobiska, H. Xie:

Supercloseness and superconvergence of stabiilized low-order finite element discretization of the stokes Problem

Math. of Comput80 (2011), 697-722

• L. He, L. Tobiska:

The two-level local projection stabilization as an enriched one-level approach

Adv. Comp. Math. (2011), DOI 10.1007/s10444-011-9188-1

• N. Ahmed, G. Matthies, L. Tobiska, H. Xie:

Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems

Comput. Methods Appl. Mech. Engrg. (2011), 1747-1756

• V. Polevikov, L. Tobiska:

ADI approach to the particle diffusion problem in magnetic fluid

Math. Modelling and Analysis16 (2011)1, 62-71

• V. Polevikov, L. Tobiska:

Influence of diffusion of magnetic particles on stability of a staticmagnetic fluid seal under the action of external pressure drop

Comm Nonlinear Sci Numer Simulat16(2011), 4021-4027

• N. Ahmed, G. Matthies, L. Tobiska:

Finite element methods of an operator splitting applied to population balance equations

J.Comp.Appl.Math.236(2011), 1604-1621

• S. Ganesan, L. Tobiska:

Stabilization by Local Projection for Convection-Diffusion and Incompressible Flow Problems

J Sci Comput 43 (2010), 326-342

• L. Tobiska, C. Winkel:

The two-level local projection stabilization as an enriched one-level approach. A one-dimensional study.

Intern.J.Num.Anal.Model.7(2010)3, 520-534

• O. Lavrova, V. Polevikov L. Tobiska:

Numerical Study of the Rosensweig Instability in a Magnetic Fluid Subject to Diffusion of Magnetic Particles

Math. Modelling and Analysis 15 (2010), 223-233

• U. Kornek, F. Müller, K. Harth, A. Hahn, S. Ganesan, L. Tobiska, R. Stannarius:

Oscillations of soap bubbles

New Journal of Physics12(2010) 073031

• S. Ganesan, L. Tobiska:

Modelling and simulation of moving contact line problems with wetting effects.

Comput. Visual. Sci. 12 (2009), 329-336

• L. Tobiska:

Recent results on local projection stabilization for concection-diffusion and flow problems.

In BAIL 2008 - Boundary and Interior Layers, ed. by A.F. Hegarty, N. Kopteva, E.O' Riordan, M. Stynes,

Lecture Notes in Computational Science and Engineering, Springer-Verlag (2009), 55-75

•S. Beresnev, V. Polevikov, L. Tobiska:

Numerical study of the influence of diffusion of magnetic particles on equilibrium shapes of a free magnetic fluid surface

Communications in nonlinear Science an numerical simulations 14 (2009), 1403-1409

• V. John, T. Mitkova, M. Roland, K. Sundmacher, L. Tobiska, A. Voigt:

Simulations of population balance systems with one internal coordinate using finite element methods.

Chemical Engineering Science 64 (2009), 733-741

• L. Tobiska:

On the relationship of local projection stabilization to other stabilized methods for one-dimentional advection-diffusion equations.

Comput. Methods Appl. Mech. Engrg. 198 (2009), 831-837

• L. Tobiska, C. Winkel:

The two-level local projection stabilization as an enriched one-level approach.

A one-dimensional study. IJNAM (accepted)

• S. Franz, L. Tobiska, H. Zarin:

A new approach to recovery of discontinuous Galerkin

Journal Comput. Math. 27 (2009) 6, 697-712

• S. Ganesan, L. Tobiska:

A coupled arbitrary Lagrangian-Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants

Journal of Computational Physics 228 (2009), 2859-2873

• S. Beresnev, V. Polevikov, L. Tobiska:

Numerical study of the influence of diffusion of magnetic particles on equilibrium shapes of a free magnetic fluid surface

Commun Nonlinear Sci Numer Simulat 14 (2009),1403-1409

• S. Ganesan, L. Tobiska:

Stabilization by local projection for convection-diffusion and incompressible flow problems

Journal Sci. Comput. (2008)

• G. Matthies, P. Skrzypacz, L. Tobiska:

Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions.

ETNA 32 (2008), 90-105

• M. Stynes, L. Tobiska:
Using rectangular Q_p elements in the SDFEM for a convection-diffusion problem with a boundary layer.

Applied Numerical Mathematics 58 (2008) 12, 1789-1802

• S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, S. Ganesan, L. Tobiska:

Quantitative benchmark computations of two-dimensional bubble dynamics

Int.J. Numer. Meth. Fluids 60 (2008) 11, 1259-1288

• A. Linke, G. Matthies, L. Tobiska:

Non-nested multi-grid solvers for mixed divergence-free Scott-Vogelius discretizations

Computing 83 (2008), 87-107

• S. Ganesan, L. Tobiska:

A finite element method for the simulation of a liquid droplet impinging on a solid surface.

Computational Sciences 42 (2008), 65-79

• S. Ganesan, L. Tobiska:

Finite element simulation of an impingging liquid droplet

Micro-Macro-Interactions in structured media and particle systems, ed. by A. Bertram and J. Tomas, Springer-Verlag (2008), 173-185

• S. Beresnev, V. Polevikov, L. Tobiska:

Numerical study of the influence of diffusion of magnetic particles on equilibrium shapes of a free magnetic fluid surface.

Micro-Macro-Interactions in structured media and particle systems, ed. by A. Bertram and J. Tomas, Springer-Verlag (2008), 277-284

• S. Ganesan, G. Matthies, L. Tobiska:

Local projection stabilization of equal order interpolation applied to the Stokes problem.

Math. Comp. 77 (2008) 264, 2039-2060

• O. Lavrova, G. Matthies, L. Tobiska:
Numerical study of soliton-like surface configurations on a magnetic fluid layer in the Rosensweig instability.
Communications in Nonlinear Science and Numerical Simulations 13 (2008), 1302-1310

• S. Ganesan, L. Tobiska:

An accurate finite element scheme with moving meshes for computing 3D-axisymmetric interface flow.

Intern. Journal Nummer. Methods Fluids 57 (2008), 119-138

• V. Polevikov, L. Tobiska:

On the solution of the steady-state diffusion problem of ferromagnetic particles in a magnetic fluid.

Mathematical Modelling and Analysis 13 (2008) 2, 233-240

• O. Lavrova, V. Polevikov, L. Tobiska:

Instability of a magnetic fluid drop in a capillary:

a numerical study. Magnetohydrodynamics 44 (2008) 2, 183-189

• G. Matthies, L. Tobiska:
Mass conservation of finite element methods for coupled flow-transport problems.
Intern. J. Comput. Sci. Math. 1 (2007) 2-4, 293-307

• L. Tobiska, S. Ganesan:

On the influence of finite element discretizations on spurious velocities in two-phase flows.

Proc. 6 th Conf. on Multiphase Flows. ICMF (2007)

• L.P. Franca, V. John, G. Matthies, L. Tobiska:
An inf-sup stable and residual-free bubble element for the oseen equations.
SIAM J. Numer. Anal. 45 (2007) 6, 2392-2407

• G. Matthies, P. Skrzypacz, L. Tobiska:
A unified convergence analysis for local projection stabilisations applied to the oseen problem.
M2AN Math. Model Numer. Anal. 41 (4), (2007), 713-742

• A. Lange, R. Richter, L. Tobiska:
Linear and nonlinear approach to the Rosensweig instability.
GAMM Mitteilungen 30, No. 1 (2007), 171-184

• C. Gollwitzer, G. Matthies, R. Richter, I. Rehberg, L. Tobiska:
The surface topography of a magnetic fluid - a quantitative comparision between experiment and numerical simulation.
J. Fluid Mech. 571(2007), 455-474

• S. Ganesan, G. Matthies, L. Tobiska:
On spurious velocities in in compressible flow problems with interfaces.
Comput. Methods Appl. Mech. Engrg. 196 (2007), 1193-1202

• S. Ganesan, L. Tobiska:

Non-isothermal spreading of a liquid droplet with dynamic contact angles on a hirizontal surface.

Proc. 6th Intern. Conf. on Multiphase Flows. ICMF (2007)

• R. Lübke, A. Seidel-Morgenstern, L. Tobiska:
Numerical method for accelerated calculation of cyclic steady state of ModiCon-SMB-processes.
Computers & Chemical Engineering 31 (2007), 250-267

• L. Tobiska:
Analysis of a new stabilized higher order finite element method for advection-diffusion equations.
Comput. Methods Appl. Mech. Engrg. 196 (2006), 538-550

• O. Lavrova, G. Matthies, T. Mitkova, V. Polevikov, L. Tobiska:
Numerical treatment of free surface problems in ferrohydrodynamics.
J. Phys.: Condens. Matter 18 (2006), S2657-2609

• S. Ganesan, L. Tobiska:

Computations on flows with interfaces using arbitrary Langrangian Eulerian method.

European Conference on Computational Fluid Synamics, ECCOMAS CFD (2006)

• G. Ziomek, D. Antos, L. Tobiska, A. Seidel-Morgenstern:
Comparision of possible arrangements of five identical columns in preparative chromatography.
J. Chromat. A, 1116 (2006), 179-188

2001-2005

• G. Matthies, L. Tobiska:
Inf-sup stable non-conforming finite elements of arbitrary order on triangles.
Numer. Math. (2005), DOI~10.1007/s00211-005-0648-8
Numer. Math. 102 (2005) 2, 293-309

• L.P. Franca, A.L. Madureira, L. Tobiska, F. Valentin:
Convergence analysis of a multiscale finite element method for singularly perturbed problems.
Multiscale Model. Simul. 4 (2005) 3, 839-866

• P. Knobloch and L. Tobiska:
On Korn's first inequality for quadrilateral nonconforming finite elements of first order approximation properties.
Intern. J. Numer. Anal. Model. 2 (2005) 4, 439-458

• G. Matthies, P. Skrzypacz, L. Tobiska:
Superconvergence of a 3d finite element method for stationary Stokes and Navier-Stokes problems.
Numer. Methods Partial Differ. Equations 21 (2005), 701-725

• V. Polevikov, L. Tobiska:
Instability of a magnetic fluid in a narrow gap between plates.
J. Magnetism and Magnetic Materials 289 (2005), 379-381

• G. Matthies, L. Tobiska:
Numerical simulation of normal-field instability in the static and dynamic case.
J. Magnetism and Magnetic Materials 289 (2005), 346-349

• V. Bashtovoi, O. Lavrova, T. Mitkova, V. Polevikov, L. Tobiska:
Flow and energy dissipation in a magnetic fluid drop around a permanent magnet.
J. Magnetism and Magnetic Materials 289 (2005), 207-210

• Q. Lin, L. Tobiska, A. Zhou:
Superconvergence and extrapolation of nonconforming low order finite elements applied to the Poisson equation.
IMA J. Numer. Anal. 25(2005), 160-181

• U. Krewer, Y. Song, K. Sundmacher, V.John, R. Lübke, G. Matthies, L. Tobiska:
Direct methanol fuel cell (DMFC): Analysis of residence time behaviour of anodic flow bed.
Chemical Engineering Science 59(2004)1, 119-130

• M. Stynes, L. Tobiska:
The SDFEM for a convection-diffusion problem with a boundary layer: optimal error analysis and enhancement of accuracy.
SIAM J. Numer. Anal. 41(2003) 5, 1620-1642

• P. Knobloch, L. Tobiska:
The P₁^mod Element: A new nonconforming finite element for convection-diffusion problems.
SIAM J. Numer. Anal. 41(2003), 436-456

• T. Mitkova, L. Tobiska:
Numerical Simulation of the flow in magnetic liquids with free surfaces.
Magnetohydrodynamics 39(2003)1, 23-28

• T. Iliescu, V. John, W. J. Layton, G. Matthies, L. Tobiska:
An assessment of models in Large eddy simulation.
Int. J. Comput. Fluid Dyn. 17 (2003) 1, 75-85

• V.G. Bashtovoi, O.A. Lavrova, V.K. Polevikov, L. Tobiska:
Computer modeling of the instability of a horizontal magnetic-fluid layer in a uniform magnetic field.
JMMM 252 (2002), 299-301

• G. Matthies, L. Tobiska:
The inf-sup condition for the mapped Q_k-P_k-1^disc element in arbitrary space dimensions.
Computing 69 (2002), 119 - 139

• V. John, P. Knobloch, G. Matthies, L. Tobiska:
Non-nested multi-level solvers for finite element discretisations of mixed problems.
Computing 68 (2002), 313 - 341

• L. P. Franca, L. Tobiska:
Stability of the residual free bubble method for bilinear finite elements on rectangular grids.
IMA J. Numer. Anal. 22 (2002) 1, 73 - 87

V. K. Polevikov, L. Tobiska:
Modelling of dynamic magnetic fluid seal affected by external pressure drop (in Russian)
Mechanics of liquids and gas 6 (2001), 42 - 51

English Translation: Modeling of a Dynamic Magneto-Fluid Seal in the Presence of a Pressure Drop.
Fluid Dynamics 36 (2001) 6, 890 - 898

• A. Thiele, T. Falk, L. Tobiska, A. Seidel-Morgenstern:

Prediction of Elution Profiles in Annular Chromatography.
Computers and Chemical Engineering 25 (2001) 7 - 8, 1089 - 1101

• M. Stynes, L. Tobiska:
Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers.
EAST-WEST J. Numer. Math. 9 (2001) 1, 59 - 76

• G. Matthies, L. Tobiska:
The streamline diffusion method for conforming and nonconforming finite elements of lowest order applied to convection-diffuion problems.
Computing 66 (2001), 343 - 364

• M. Stynes, L. Tobiska:
The streamline-diffusion method for nonconforming Q₁^rot-elements on rectangular tensor product meshes.
IMA Journal of Numerical Analysis 21 (2001), 123 - 142

before 2001

• S. I. Petrova, L. Tobiska, P. S. Vassilevski:
Multigrid Methods Based on Matrix-Dependent Coarse Spaces for Nonconforming Streamline-Diffusion Finite Element Discretization of Convection-Diffusion Problems.
EAST-WEST J. Numer. Math. 8 (2000) 3, 223 - 242

• V. John, L. Tobiska:
A Coupled Multigrid Method for Nonconforming Finite Element Discretizations of the 2D-Stokes Equation.
Computing 64 (2000), 307 - 321

• V. John, L. Tobiska:
Numerical Performance of Smoothers in Coupled Multigrid Methods for the Parallel Solution of the Incompressible Navier-Stokes Equations.
Int. J. Numer. Meth. Fluids 33 (2000), 453 - 473

• P. Knobloch, L. Tobiska:
Stabilization methods of bubble type for the Q₁/Q₁-element applied to the incompressible Navier-Stokes equation.
M²AN 34 (2000) 1, 85 - 107

• P. Knobloch, L. Tobiska:
Analysis of a mathematical model related to Czochalski crystal growth.
Abstract and Applied Analysis 3 (1998), 319 - 342

• V. V. Shaidurov, L. Tobiska:
The convergence of the cascadic conjugate-Gradient method applied to elliptic problems in domains with re-entrant corners. <bR

• M. Stynes, L. Tobiska:
A Finite Difference Analysis of a Streamline Diffusion Method on a Shishkin Mesh.
Numerical Algorithms 18 (1998) 3 - 4, 337 - 360

• W. Layton, L. Tobiska:
A two-level method with backtracking for the Navier-Stokes equations.
SIAM J. Numer. Anal. 35 (1998) 5, 2035 - 2054

• V. John, G. Matthies, F. Schieweck, L. Tobiska:
A Streamline-Diffusion Method for Nonconforming Finite Element Approximations Applied to Convection-Diffusion Problems.
Comput. Meth. Appl. Mech. Engrg. 166 (1998), 85 - 97

• R. D. Lazarov, L. Tobiska, P. S. Vassilevski:
Streamline diffusion least-squares mixed finite element method for convection-diffusion problems.
EAST-WEST J. Numer. Math. 5 (1997) 4 , 249 - 264

• V. John, J. Maubach, L. Tobiska:
Nonconforming Streamline-Diffusion-Finite-Element-Methods for Convection-Diffusion Problems.
Numer. Math. 78 (1997), 165 - 188

• F. Schieweck, L. Tobiska:
An Optimal Order Error Estimate for an Upwind Discretization of the Navier-Stokes Equations.
Numer. Methods for Partial Differential Equations 12 (1996), 407 - 421

• L. Tobiska, R. Verfürth:
Analysis of a Streamline Diffusion Finite Element Method for the Stokes and Navier-Stokes Equations.
SIAM J. Numer. Anal. 33 (1996) 1, 107 - 127

• V. V. Shaidurov, L. Tobiska:
Special integration formulas for a convection-diffusion problem.
EAST-WEST J. Num. Math. 3 (1995) 4, 281 - 299

• L. Tobiska:
A note on the artificial viscosity of numerical schemes.
Comp. Fluid Dyn. 5 (1995), 281 - 290

• M. Stynes, L. Tobiska:
Necessary L²-uniform convergence conditions for difference schemes for two dimensional convection-diffusion problems.
Computers Math. Applic. 29 (1995) 4, 45 - 53

• V. V. Shaidurov, L. Tobiska:
A Survey of Finite Element Spaces for Incompressible Viscous Flows Satisfying the Stability Condition. Part I. (in Russian)
Mathematical Modelling 6 (23) (1992) 4, 123 - 140

• W. Grambow, G. Lube, L. Tobiska:
Numerische Lösung des instationären, inkompressiblen Navier-Stokes Modells.
Technische Mechanik 12 (1991) 3, 149 - 158

•L. Tobiska, G. Lube:
A modified streamline diffusion type method for solving stationary Navier-Stokes equations.
Num. Math. 59 (1991), 13 - 29

• L. Tobiska:
Finite Element Methods of Upwind Type for the Navier-Stokes Equations.
ZAMM 71 (1991) 6, 678 - 679

• G. Lube, L. Tobiska:
A nonconforming finite element methods of streamline diffusion type for the incompressible Navier-Stokes equations.
J. Comp. Math. 8 (1990) 2, 147 - 158

• L. Tobiska, A. Thiele:
A weighted upwind method for solving the stationary Navier-Stokes equation.
WZ TUM 33 (1989) 6, 13 - 20

• H. Goering, L. Tobiska:
Finite element methods for singularly perturbed elliptic boundary value problems.
Zeitschrift für Analysis und ihre Anwendungen 8 (1989) 1, 13 - 23

• F. Schieweck, L. Tobiska:
A nonconforming finite element method of upstream type applied to the stationary Navier-Stokes-equations.
Math. Modelling and Numer. Anal. 23 (1989) 4, 627 - 647

• L. Tobiska:
Zur Konstruktion und Verwendung diskretdivergenzfreier Finiter Elemente für die Lösung der Navier-Stokes-Gleichungen.
WZ TUM 31 (1987), 77 - 81

• L. Tobiska, F. Schieweck:
Eine upwind FEM zur Lösung des stationären Navier-Stokes Problems.
WZ TUM 31 (1987) 5, 73 - 76

• G. Koeppe, H.-G. Roos, L. Tobiska:
An enclosure generating modification of the method of discretization in time.
Comment. math. carol. 28 (1987) 3, 441 - 447

• L. Tobiska:
Nichtlineare singulär gestörte Differentialgleichungen elliptischen Typs.
WZ TH Leuna-Merseburg 27 (1985) 5, 561 - 566

• L. Tobiska, H.-G. Roos:
Singularly perturbed elliptic problems of second order with a singular line.
Zeitschrift für Analysis und ihre Anwendung Bd. 2 (6), (1983), 563 - 571

• L. Tobiska:
Diskretisierungsverfahren zur Lösung singulär gestörter Randwertprobleme.
ZAMM 63 (1983), 115 - 123

• L. Tobiska:
Die asymptotische Lösung einiger Probleme des konvektiven Wärmeaustausches stationärer Strömungen.
Wiss. Z. TH Magdeburg 25 (1981) 4, 29 - 32

• L. Tobiska:
A priori Abschätzungen für singulär gestörte elliptische Probleme zweiter Ordnung.
Beiträge zur Analysis 17 (1981), 41 - 48

• G. Lube, L. Tobiska:
Singulär gestörte elliptische Probleme beliebiger Ordnung mit Typänderung.
Math. Nachrichten 98 (1980), 123 - 134

• L. Tobiska, G. Lube:
Die asymptotische Lößung singulär gestörter elliptischer Probleme 2. Ordnung.
Wiss. Z. TH Magdeburg 24 (1980) 5, 21 - 24

• H.-G. Roos, L. Tobiska:
Die asymptotische Lösung spezieller Wärmeleitungsprobleme in Strömungen.
Wiss. Z. TH Magdeburg 23 (1979) 6, 575 - 577

• L. Tobiska:
Die asymptotische Lösung einer linearen elliptischen Differentialgleichung mit Wendepunkten.
Beiträge zur Analysis 13 (1979), 77 - 82

• L. Tobiska:
Asymptotische Lösung der ebenen Wärmebilanzgleichung für stationäre Grenzschichtströmungen.
Wiss. Z. TH Magdeburg 21 (1977) 7, 687 - 688