Homepage Prof. Roos

Homepage of Prof. Dr. rer. nat. habil. H.-G. Roos

Address: Prof. Dr. rer. nat. habil. H.-G. Roos
Institute of Numerical Mathematics
Department of Mathematics
Technical University of Dresden

Phone: (+49)(0351) 463 35049, Fax: (+49) (0351) 463 34268

E-Mail:

Position: Professorship Numerical methods for Partial Differential Equations

Main field of interests:

Numerical analysis of discretisation methods for pde's
Singularly perturbed differential equations
Applications of splines and wavelets for differential equations
Reliable error estimators
Flow problems

Conferences:

Workshop Numerical methods for problems with layer phenomena, Cyprus , 23.5. - 24.5.2013

Lectures Summer Semester 2013:

Numerical Mathematics 2: see homepage R. Vanselow →

Numerical methods for partial differential equations 2: see homepage M. Schopf →

Seminar of the Institute

Publications:

Papers

Books and Proceedings

Goering, H.; Roos, H.-G.; Tobiska, L.:
Die Finite-Elemente-Methode für Anfänger.
Wiley, Berlin, 2010.    Link to the publisher

Roos, H.-G.; Stynes, M.; Tobiska, L.:
Robust Numerical Methods for Singularly Perturbed Differential Equations -- Convection-Diffusion-Reaction and Flow Problems.
Springer Series in Computational Mathematics , Vol. 24, 2nd ed., 2008, 616 pages, ISBN: 978-3-540-34466-7
Table of Contents   Link to the publisher

Grossmann, C.; Roos, H.-G.; Stynes, M.:
Numerical treatment of partial differential equations.
Springer, Heidelberg-Berlin, 2007.    Link to the publisher

Publications:

Papers:2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 1999 1998 1997

2013:

(with Z. Ucelaz)
Qualocation for a singularly perturbed boundary value problem.
JCAM, 237(2013), 556-564

(with M. Vlasak)
An optimal uniform a priori error estimate for an unstaedy singularly perturbed problem.
aacepted in IJNAM

(with L. Teofanov, Z. Ucelaz)
Graded meshes for higher order FEM.
submitted

2012:

Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012.
ISRN Applied Mathematics, vol. 2012, ID 379547, doi:10.5042/2012/379547

(with S. Franz, A. Wachtel)
A C^0 interior penalty method for a fourth-order elliptic problem on a layer-adapted mesh.
submitted

(with L. Ludwig)
Finite element superconvergence on Shishkin meshes for convection-diffusion problems with corner singularities.
submitted

(with M. Schopf)
Error estimation in energy norms: Is it necessary to fit the mesh to boundary layers ?
submitted

(with S. Franz)
Error estimation in a balanced norm for a convection-diffusion problem with characteristic boundary layers.
submitted

(with M. Schopf)
Convergence and stability in balanced norms of finite element mathods on Shishkin meshes for reaction-diffusion problems.
submitted

(with M. Vlasak)
Optimal error estimates for nonstationary singularly perturbed problems for low order discretization orders.
ACC Journal, TU Liberec, XVIII 4/2012, 146-152

Special features of strongly coupled systems of convection-diffusion equations with two small parameters.
Appl. Math. Letters, 25(2012), 1127-1130

(with S. Franz, R. Gaertner, A.Voigt)
A note on the convergence analysis of a diffuse-domain approach.
CMAM, 12(2012), 153-167

(with L. Ludwig)
Superconvergence for convection-diffusion problems with low regularity.
Proc. of Applications of Mathematics 2012, Prague 2-5, 2012, 173-187

(with M. Schopf)
Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D.
Appl. of Math., 57(2012), 97-108

(with T. Linss, M. Schopf)
Nitsche-mortaring for singularly perturbed convection-diffusion problems.
Advances Comput. Math., 4(2012), 581-603

2011:

(with S. Franz)
The capriciousness of numerical methods for singular perturbations.
SIAM review, 53, 2011, N0 1, 157-173

(with C. Großmann, L. Ludwig)
Layer-adapted methods for a singularly perturbed singular problem.
CMAM, 11 (2011), 192-205

(with C. Reibiger)
Numerical analysis of a strongly coupled system of two convection-diffusion equations with full layer interaction.
ZAMM 91(2011), 537-543

(with Ch. Reibiger)
Numerical analysis of a system of singularly perturbed convection-diffusion equations related to optimal control.
NMTMA, 4(2011), 562-575

(with M. Krizek)
Two-sided bounds of the discretization error for finite elements.
ESAIM, 45(2011), 915-924

(with M. Schopf)
Finite elements on locally uniform meshes for convection-diffusion problems with boundary layers.
Computing, 92(2011), 285-296

(with Ch. Grossmann, R. K. Mohanty)
A direct higher order discretization in singular perturbations via domain split--a computational approach.
Appl. Math. Comp., 217(2011), 9302-9312

2010:

(with V. Dolejsi)
BDF-FEM for parabolic singularly perturbed problems with exponential layers on layer-adapted meshes in space.
NeuralParallelSci. Comput., 18(2010), no.2, 221-235

(with S. Franz, T. Linss, S. Schiller)
Uniform convergence of finite element methods with edge stabilization on Shishkin meshes.
J. Comput. Math.,28(2010),32-44

(with l. Kaland)
Parabolic singularly perturbed problems with exponential layers: robust discretizations using finite elements in space on Shishkin meshes.
IJNAM, 7(2010), nr 3, 593-606

Two remarks on numerical methods for singularly perturbed problems.
Preprint MATH-NM-06-2010, TU Dresden

2009:

Stabilized FEM for convection-diffusion problems on layer-adapted meshes.
J. Comput. Math., 27(2009), 266-279
(with S. Franz, F. Liu, M. Stynes, A. Zhou)
The combination technique for two-dimensional convection-diffusion problems with exponential layers.
Applications of Math., 54(2009), 203-223

2008:

(with L. Teofanov)
A singularly perturbed problem with two small parameters II:
The Galerkin finite element method on a Shishkin mesh.
J. Comput. Appl. Math., 212(2008), 374-389
(with T. Apel)
Remarks on the analysis of finite element methods on a Shishkin mesh: are Scott-Zhang interpolants applicable?
Preprint MATH-NM-06-2008, TU Dresden

(with S. Franz and T. Linss) Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers.
Appl. Numer. Math., 58(2008),1818-1829

2007:

(with R. Vanselow) A comparison of four- and five-point difference approximations for stabilizing the one-dimensional stationary convection-diffusion equation.
ETNA, 32(2008), 63-75
A link between local projection stabilizations and the continuous interior penalty method for convection-diffusion problems.
Preprint MATH-NM-05-07 pdf-file
(with H. Zarin) A supercloseness result for the discontinuous Galerkin stabilization of convection-diffusion problems.
Numer. Meth. f. Partial Diff. Equ., 23(2007), 1560-1576

(with L. Teofanov) A singularly perturbed problem with two parameters I:
Solution decomposition
J. Comput. Appl. Math., 206(2007), 1082-1097

2006:

Error estimates for linear finite elements on Bakhvalov-type meshes.
Applications of Mathematics, 51(2006),63-72

Superconvergence on a hybrid R-T-mesh for singularly perturbed problems with exponential layers.
ZAMM, 86(2006), 649-655

2005:

(with H. Zarin) Interior penalty discontinuous approximations of a convection-diffusion
problem with parabolic layers.
Numerische Mathematik, 100(2005),735-759

2004:

A uniformly convergent scheme for a singularly perturbed eigenvalue problem.
Proceedings of BAIL 2004

(with T. Linss) Analysis of a finite difference scheme for a singularly perturbed problem with two small parameters.
JMAA, 289(2004), 355-366

(with H. Zarin) The discontinuous Galerkin method for singularly perturbed problems.
in: Numerical Mathematics and advanced Applications, eds.: M. Feistauer et all., Springer 2004, 736-745

2003:

On the streamline-diffusion stabilization for convection-diffusion problems
Report MATH-NM-05(2003), TUD
(with H. Zarin) The streamline-diffusion method for a convection-diffusion problem with a point source.
JCAM , 150(2003), 109-128
(with Z. Uzelac) The SDFEM for a convection-diffusion problem with two small parameters.
CMAM, 3(2003), No.3, 443-458
(with H.Zarin) The discontinous Galerkin finite element method for singularly perturbed problems.
in: Lecture Notes in Comput. Science and Engin., vol. 35 (2003), 246-267

(with H. Zarin) Some properties of the discontinuous Galerkin-method for reaction-diffusion and
convection-diffusion problems in 1D.
Novi Sad J. Math., 33(2003), no 2, 33-42

2002:

Optimal uniform convergence of basic schemes for elliptic problems with strong parabolic boundary layers.
JMAA, 267(2002), 194-208

(with H. Zarin) A second order scheme for singularly perturbed differential equations with discontinuous source term.
Journal Numerical Math., 10(2002), 275-289

(with D. Wollstein, T. Linss) A uniformly accurate FVM discretization for a convection-diffusion problem.
ETNA 13 (2002), 1-11

2001:

(with A. Froehner, T. Linss) Defect correction on Shishkin.type meshes.
Numerical Algorithms, 26(2001), 281-299
(with T. Linss) Gradient recovery for singularly perturbed boundary value problems (II).
M3AS, 11, No.7(2001), 1169-1179
(with T. Linss, R. Vulanovic) Uniform pointwise convergence on Shishkin-type meshes for convection-diffusion problems.
SINUM , 38, 897-912 (2001)
(with T.Linss, D. Schneider) Uniform convergence of an upwind finite element method on layer-adapted grids.
Computer Meth. Appl. Mech. Eng., 190 (2001), 4519-4530
(with T.Linss) Gradient recovery for singularly perturbed problems (I)
Computing, 66, 163-178 (2001)
On a stabilization effect of thin submeshes for convection-diffusion-problems.
ZAMM , 81 (2001), 637-639
(with A. Froehner ) The uniform convergence of a defect correction method on a Shishkin mesh.
Appl. Num. Math. , 37, 79-94 (2001)

1999:

(with T.Skalicky) Anisotropic mesh refinement for problems with internal and boundary layers.
International J. f. Numer. Methods in Engineering, 46 (1999), 1933-1953
(with T. Linss) Sufficient conditions for uniform convergence on layer adapted grids.
Computing, 63, 27-45 (1999)
(with B. Bagaev) The finite element method on an adapted mesh for a two-dimensional convection-diffusion problem.
Sibirian Numerical J., no 4, 1999, 309-320

1998:

(with T. Skalicky) Galerkin/Least-squares finite element method for convection-dominated problems on Gartland-type meshes.
Report MATH-NM-12, 1998, TU Dresden
Layer-adapted grids for singularly perturbed boundary value problems,
Z. Angew. Math. Mech., 78(5): 291-309,1998

1997:

(with M.Dobrowolski):A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes,
Zeitschrift für Analysis u. Anw., 16(4), 1001-1012, 1997
(with T.Skalicky):A comparison of the finite element method on Shishkin and Gartland-type meshes for convection-diffusion problems.
CWI Quarterly, 10(3&4), 277-300, 1997

Books and Proceedings:

(with M. Stynes and L. Tobiska)
Robust Numerical Methods for Singularly Perturbed Differential Equations -- Convection-Diffusion-Reaction and Flow Problems.
Springer Series in Computational Mathematics , Vol. 24, 2nd ed., 2008, 616 pages, ISBN: 978-3-540-34466-7

(with Ch. Grossmann, M. Stynes)
Numerical treatment of partial differential equations
Springer-Verlag, Heidelberg-Berlin, 2007, 596 pages, ISBN 978-3-540-71582-5

(with Ch. Grossmann)
Numerische Behandlung partieller Differentialgleichungen
Teubner-Verlag, Stuttgart, November 2005, third extended edition, 570 pages, ISBN 3-519-22089-X

(with H. Schwetlick)
Numerische Mathematik: Das Grundwissen für jedermann (Teubner, September 99)

(with M.Stynes, L.Tobiska)
Numerical methods for singularly perturbed differential equations,
350 pages, Springer-Verlag, 1996

(with Ch. Grossmann)
Numerik partieller Differentialgleichungen,
478 pages, Teubner-Verlag, Stuttgart, 1992, second edition 1994

(with A.Felgenhauer, L.Angermann, eds.)
Numerical Methods in Singularly Perturbed Problems,
University of Technology Dresden, 1991

(with E.Adams, R.Ansorge, Ch.Grossmann, eds.)
Discretization in Differential Equations and Enclosures, Akademie-Verlag, Berlin 1987

(with H.Goering, L.Tobiska)
Finite-Element-Methode,
Akademie-Verlag, Berlin 1985 (third extended edition 1993)

(with H.Goering, A.Felgenhauer, G.Lube, L.Tobiska)
Singularly perturbed differential equations,
Akademie-Verlag, Berlin 1983

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Department

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Last modified: August, 2008
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