Weierstrass Institute
for Applied Analysis and Stochastics

Papers of Jürgen Fuhrmann

Journal Papers

M. Augustin, A. Caiazzo, A. Fiebach, J. Fuhrmann, V. John, A. Linke, and R. Umla.
An assessment of discretizations for convection-dominated convection-diffusion equations.
Comp. Meth. Appl. Mech. Engrg., 200:3395-3409, 2011.

2

J. Fuhrmann, H. Zhao, H. Langmach, Y. E. Seidel, Z. Jusys, and R. J. Behm.
The role of reactive reaction intermediates in two-step heterogeneous electrocatalytic reactions: A model study.
Fuel Cells, 11(4):501-510, 2011.

3

J. Fuhrmann, A. Linke, and H. Langmach.
A numerical method for mass conservative coupling between fluid flow and solute transport.
Applied Numerical Mathematics, 61(4):530 - 553, 2011.

4

J. Fuhrmann, A. Fiebach, A. Erdmann, and P. Trefonas.
Acid diffusion effects between resists in freezing processes used for contact hole patterning.
Microel. Engrg., 87(5-8):951-954, 2010.
Proc. MNE 2009.

5

A. Bradji and J. Fuhrmann.
Error estimates of the discretization of linear parabolic equations on general nonconforming spatial grids.
CRAS, 348(19-20):1119-1122, 2010.

6

H. Si, K. Gärtner, and J. Fuhrmann.
Boundary conforming Delaunay mesh generation.
Comput. Math. Math. Phys., 50:38-53, 2010.

7

J. Fuhrmann, A. Linke, H. Langmach, and H. Baltruschat.
Numerical calculation of the limiting current for a cylindrical thin layer flow cell.
Electrochimica Acta, 55:430-438, 2009.

8

J. Fuhrmann, A. Fiebach, M. Uhle, A. Erdmann, Ch. Szmanda, and C. Truong.
A model of self-limiting residual acid diffusion for pattern doubling.
Microel. Engrg., 86(4-6):792-795, 2009.
Proceedings MNE 2008.

9

J.Fuhrmann, H.Zhao, E.Holzbecher, H.Langmach, M.Chojak, R.Halseid, Z.Jusys, and R Behm.
Experimental and numerical model study of the limiting current in a channel flow cell with a circular electrode.
Phys. Chem. Chem. Phys., 10:3784 - 3795, 2008.

10

J.Fuhrmann, H. Zhao, E. Holzbecher, and H. Langmach.
Flow, transport and reactions in a thin layer flow cell.
Journal of Fuel Cell Science and Technology, 5(2):021008, 2008.

11

R. Eymard, J. Fuhrmann, and K. Gärtner.
A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local Dirichlet problems.
Numerische Mathematik, 102(3):463 - 495, 2006.

12

F. Magri, U. Bayer, C. Jahnke, V. Clausnitzer, H.-J. Diersch, J. Fuhrmann, P. Möller, A. Pekdeger, M. Tesmer, and H. Voigt.
Fluid-dynamics driving saline water in the north east german basin.
International Journal of Earth Sciences, 94(5-6):1056-1069, 2005.

13

B. Tollkühn, M Uhle, J. Fuhrmann, K. Gärtner, A. Heubner, and A. Erdmann.
Benchmark of a lithography simulation tool for next generation applications.
Microelectronic Engineering, 83(4-9):1142-1147, 2006.
Proceedings MNE 2005.

14

M Efendiev, J. Fuhrmann, and S. Zelik.
The long-time behaviour of the thermoconvective flow in a porous medium.
Math. Methods Appl. Sci., 27(4):907-930, 2004.

15

J. Divisek, J. Fuhrmann, K. Gärtner, and R. Jung.
Performance modeling of a direct methanol fuel cell.
J. Electrochem. Soc., 150(6):A811-A825, 2003.

16

J. Fuhrmann.
Existence and uniqueness of solutions of certain systems of algebraic equations with off-diagonal nonlinearity.
Appl. Numer. Math., 37(3):359-370, 2001.

17

J. Fuhrmann and H. Langmach.
Stability and existence of solutions of time-implicit finite volume schemes for viscous nonlinear conservation laws.
Appl. Numer. Math., 37(1-2):201-230, 2001.

18

J. Fuhrmann, D. Hömberg, and M. Uhle.
Numerical simulation of induction hardening of steel.
COMPEL, 18(3):482-494, 1999.
Selected Papers from the 8th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, Graz, Austria, 1998.

19

J. Fuhrmann and D. Hömberg.
Numerical simulation of surface heat treatments.
Int. J. Numer. Methods Heat Fluid Flow, 6:705-724, 1999.

Submitted

1

A. Bradji and J. Fuhrmann.
Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes.
Preprint 1660, WIAS Berlin, 2011.
To appear in Applications of Mathematics.

2

R. Eymard, J. Fuhrmann, and A. Linke.
MAC schemes on triangular Delaunay meshes.
Preprint 1654, WIAS Berlin, 2011.

3

Ch. Batallion, F.Bouchon, C. Chainais-Hillairet, J. Fuhrmann, E. Hoarau, and R. Touzani.
Numerical methods for the simulation of a corrosion model in a nuclear waste deep repository.
WIAS Preprint 1575 and hal-00545552, submitted.

4

Th. Koprucki, R. Eymard, and J. Fuhrmann.
Convergence of a finite volume scheme to the eigenvalues of a schrödinger operator.
Technical report, WIAS Berlin, 2007.
WIAS Preprint no. 1260, submitted.

Selected Contributions to Proceedings and Compilations

1

J. Fuhrmann, A. Linke, and H. Langmach.
Mass conservative coupling between fluid flow and solute transport.
In J. Fořt, J. Fürst, J. Halama, R. Herbin, and F. Hubert, editors, Finite Volumes for Complex Applications VI, pages 475-483. Springer, 2011.

2

R. Eymard, J. Fuhrmann, and A. Linke.
MAC schemes on triangular Delaunay meshes.
In J. Fořt, J. Fürst, J. Halama, R. Herbin, and F. Hubert, editors, Finite Volumes for Complex Applications VI, pages 399-407. Springer, 2011.

3

A. Erdmann, F. Shao, J. Fuhrmann, A. Fiebach, G. P. Patsis, and P. Trefonas.
Modeling of double patterning interactions in litho-cure-litho-etch (LCLE) processes.
In Proc. SPIE, volume 7640, page 76400B, 2010.

4

J. Fuhrmann, A. Fiebach, and G. P. Patsis.
Macroscopic and stochastic modeling approaches to pattern doubling by acid catalyzed cross-linking.
In Proc. SPIE, volume 7639, page 76392I, 2010.

5

J. Fuhrmann and K. Gärtner.
Modeling of two-phase flow and catalytic reaction kinetics for DMFCs.
In S. Paddison and K. Promislow, editors, Device and Materials Modeling in PEM Fuel Cells, volume 113 of Topics in Applied Physics, pages 297-316. Springer, 2009.

6

A. Bradji and J. Fuhrmann.
Some error estimates in finite volume methods of parabolic problems.
In R. Eymard and J.-M. Herard, editors, Finite Volumes for Complex Application V, pages 233-241. ISTE Ltd, 2008.

7

J. Fuhrmann, H. Zhao, H. Langmach, and E. Holzbecher.
Modeling and simulation of coupled species transport, porous electrode effects and catalytic reactions in a rectangular flow cell.
In R. Eymard and J.-M. Herard, editors, Finite Volumes for Complex Applications V, pages 423-431. ISTE Ltd, 2008.

8

Th. Koprucki, H.-Ch. Kaiser, and J. Fuhrmann.
Electronic states in semiconductor nanostructures and upscaling to semi-classical models.
In A. Mielke, editor, Analysis, Modeling and Simulation of Multiscale Problems, pages 365-394. Springer, 2006.

9

J. Fuhrmann.
Evaluation of numerical fluxes for a locally exact finite volume scheme using hypergeometric functions.
In Finite Volumes in Complex Applications IV: Proc. Marrakech, pages 337-344. HERMES, Paris, 2005.

10

J. Fuhrmann and M. Petzoldt.
Robust error estimators for interface problems occuring in transport processes in porous media.
In W. Jäger and H.J. Krebs (eds.), editors, Mathematics -- Key Technology for the Future, Frankfurt am Main, December 11-12, 2000, pages 127-136. Springer, 2003.

11

J. Fuhrmann.
Multiphysics systems solution by time-implicit Voronoi box finite volumes.
In Finite Volumes in Complex Applications III: Proc. Porquerolles, pages 551-559, Paris, 2002. HERMES.
ISBN-1-9039-9634-1.

12

J. Fuhrmann, D. Hömberg, and J. Sokolowski.
Modeling, simulation and control of laser heat treatments.
In Optimal control of complex structures (Oberwolfach, 2000), volume 139 of Internat. Ser. Numer. Math., pages 71-82. Birkhäuser, 2002.

Other Contributions to Proceedings and Compilations

1

M. Ehrhardt, J. Fuhrmann, A. Linke, and E. Holzbecher.
Mathematical modeling of channel-porous layer interfaces in PEM fuel cells.
In B. Davat and D. Hissel, editors, Fundamentals and Developments of Fuel Cells, Proc. Nancy, Dec. 10-12, 2008.
ISBN 978-2-7466-0413-1.

2

E. Holzbecher, J. Fuhrmann, H. Zhao, H. Langmach, and K. Gärtner.
Modelling of direct methanol fuel cells for microelectronical applications.
In World Hydrogen Technologies Convention (WHTC2007), Montecatine Terme, Italy, November 2007.

3

E. Holzbecher, J. Fuhrmann, H. Zhao, and H. Langmach.
A model of thin layer flow cells aimed at kinetic parameter estimation.
In European Fuel Cell Technology and Applications Conference (EFC2007), Rome, Italy, December 2007.

4

J. Divisek, R. Jung, K. Gärtner, and J. Fuhrmann.
Numerical Simulation of Direct Methanol Fuel Cells (DMFC).
In Proceedings 3rd European Congress of Chemical Engineering, Nuremberg, 26.-28. June 2001, 2001.

5

J. Fuhrmann and H. Langmach.
Mass conservative numerical solution of subsurface transport problems.
In K.P. Holz, W. Bechteler, S.S.Y. Wang, and M. Kawahara, editors, Proceedings of the 3rd International Conference on Hydroscience and Engineering, BTU Cottbus, 31.8.-3.9.1998, volume 3 of Advances in Hydroscience and Engineering, Cottbus, 1998.
URL http://www.bauinf.tu-cottbus.de/ICHE98/Proceedings/Welcome.html.

6

J. Fuhrmann.
Finite volume methods for the discretization of flow and transport phenomena.
In Fachtagung Grafikgestützte Grundwassermodellierung, 27.-28. Mai 1998, pages 25-31, Berlin, 1998. WASY GmbH (Hrsg.).

7

J. Fuhrmann, Th. Koprucki, and H. Langmach.
pdelib: An open modular tool box for the numerical solution of partial differential equations. Design Patterns.
In W. Hackbusch and G. Wittum;, editors, Proceedings of the 14th GAMM Seminar Kiel on Concepts of Numerical Software, January 23-25, 1998. Kiel, 2001.

8

J. Fuhrmann.
Algebraic multigrid methods -- a comparision.
In J. Wang, M.B. Allen, B.M. Chen, and T. Mathew, editors, Iterative Methods in Scientific Computing (Proc. Jackson Hole WY, July 9-12 1997), volume 4 of IMACS Series in Computational and Applied Mathematics, pages 155-161, 1997.

9

J. Fuhrmann.
Numerical solution schemes for nonlinear diffusion problems based on Newton's method.
In K. Mikula A. Handlovicovaá, M.Komorníková, editor, ALGORITMY '97, 14th Conference on Scientific Computing, Zuberec, Slovakia, September 2-5, 1997, Contributed papers and posters, pages 32-42. Slovak Technical University, Bratislava, 1997.
ISBN 80-227-0977-8.

10

J. Fuhrmann.
Outlines of a modular algebraic multigrid method.
In O. Axelsson and B. Polman, editors, Proceedings of the Conference on Algebraic Multilevel Iteration Methods, Nijmegen, 13.-15.6.1996, pages 141-153, Nijmegen, 1996. Kath. Univ. Nijmegen.

11

J. Fuhrmann.
On numerical solution methods for nonlinear parabolic problems.
In R. Helmig, W. Jäger, W. Kinzelbach, P. Knabner, and G. Wittum, editors, Modeling and Computation in Environmental Sciences. Proceedings of the First GAMM-Seminar at ICA Stuttgart, October 12-13,1995, volume 59 of Notes on Numerical Fluid Mechanics, pages 170-180, Braunschweig, 1997. Vieweg.

12

J. Fuhrmann.
On the numerical solution of the equation of saturated/unsaturated flow in porous media.
In A. Peters et al., editors, Computational methods in water resources X, Dordrecht, 1994. Kluwer.
Proceedings Heidelberg, July 1994.

13

J. Fuhrmann and K. Gärtner.
On matrix data structures and the stability of multigrid algorithms.
In P. W. Hemker and P. Wesseling, editors, Contributions to multigrid. A selection of contributions to the Fourth European Multigrid Conference, Amsterdam, July 6-9, 1993, Amsterdam, 1994. CWI.
CWI Tract 103.

14

J. Fuhrmann and K. Gärtner.
Multigrid becomes a competitive algorithm for some 3D device simulation problems.
In Proceedings of SISDEP, Wien 1993, pages 421-424, Wien, 1993. Springer Verlag.

15

J. Fuhrmann and K. Gärtner.
Incomplete factorizations and linear multigrid algorithms for the semiconductor device equations.
In R. Beauwens and P. de Groen, editors, Proccedings of the IMACS international symposium on iterative methods in linear algebra, pages 493-503, Amsterdam, 1992. Elsevier.

16

J. Fuhrmann.
Calculation of saturated-unsaturated flow in porous media with a Newton-multigrid method.
In S. Hengst, editor, GAMM-Seminar on Multigrid Methods, Gosen, September 1992, Berlin, 1993. Institut für Angewandte Analysis und Stochastik.
Report No. 5.

17

J. Fuhrmann and K. Gärtner.
A multigrid method for the solution of a convection -- diffusion equation with rapidly varying coefficients.
In W. Hackbusch and U. Trottenberg, editors, Proceedings of the Third European Multigrid Conference, October 1 - 4,1990, Bonn, Germany, volume 98 of ISNM, Basel, 1991. Birkhäuser Verlag.

18

J. Fuhrmann.
An interpretation of the Scharfetter-Gummel scheme as a mixed finite element discretization.
In G. Telschow, editor, Fourth Multigrid Seminar, Unterwirbach, May 1989, Berlin, 1990. Karl-Weierstraß-Institut für Mathematik.
Report R-MATH-03/90.

19

J. Fuhrmann.
Multigrid FAS methods for the solution of systems of nonlinear partial differential equations occuring in semiconductor device simulation.
In G. Telschow, editor, Third Multigrid Seminar, Biesenthal, May 2-6,1988. Karl-Weierstraß-Institut für Mathematik, Berlin, 1989.
Report R-MATH-03/89.

Theses

1

J. Fuhrmann.
Zur Verwendung von Mehrgitterverfahren bei der numerischen Behandlung elliptischer partieller Differentialgleichungen zweiter Ordnung mit variablen Koeffizienten.
PhD thesis, Technische Universität Chemnitz-Zwickau, 1994.
Verlag Shaker, Aachen 1995, ISBN 3-8265-0522-0.

2

J. Fuhrmann.
Die endliche Erzeugtheit des plurikanonischen Rings von Mannigfaltigkeiten des allgemeinen Typs der Dimensionen 2 und 3, 1984.
Diplomarbeit (in Russisch), Mechanisch-Mathematische Fakultät der Moskauer Staatlichen Universität.

Miscellaneous

1

U. Bayer, V. Clausnitzer, and J. Fuhrmann.
Unsteady thermal convection in the North-East German Basin.
Technical report, WIAS Berlin, 2002.
Preprint No. 741, submitted.

2

V. Clausnitzer, U. Bayer, and J. Fuhrmann.
Large-scale thermal convective instability in sedimentary basins.
Eur. Geophys. Soc., Geophys. Res. Abstracts, HS02-02, 2001.

3

J. Fuhrmann.
A modular algebraic multilevel method.
Technical report, Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, 1995.
Preprint no. 203.

4

J. Fuhrmann.
On the convergence of algebraically defined multigrid methods.
Technical report, Institut für Angewandte Analysis und Stochastik, 1992.
Preprint no. 3.

5

K. Gärtner, G. Telschow, F. Grund, H. Langmach, J. Fuhrmann, H. Szillat, and C. Keusch.
MEDEA-Anwendungsbeschreibung.
technical documentation, Karl-Weierstraß-Institut für Mathematik, Berlin, 1989.
unpublished.