Publikationen
2023
An unconditionally stable finite element scheme for anisotropic curve shortening flow
Deckelnick, Klaus; Nürnberg, Robert
In: Archivum mathematicum - Brno : Masaryk Univ., Bd. 59 (2023), Heft 3, S. 263-274
Discrete hyperbolic curvature flow in the plane
Deckelnick, Klaus; Nürnberg, Robert
In: SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics - Philadelphia, Pa. : SIAM, Bd. 61 (2023), Heft 4, S. 1835-1857
A novel finite element approximation of anisotropic curve shortening flow
Deckelnick, Klaus; Nürnberg, Robert
In: Interfaces and free boundaries - Zürich : European Mathematical Soc. Publ. House, Bd. 25 (2023), Heft 4, S. 671-708
Interfaces - modeling, analysis, numerics
Bänsch, Eberhard; Deckelnick, Klaus; Garcke, Harald; Pozzi, Paola
In: Cham: Birkhäuser Springer, 2023, 1 Online-Ressource - (Oberwolfach seminars; volume 51), ISBN: 978-3-031-35550-9
2022
A novel W1,∞ approach to shape optimisation with Lipschitz domains
Deckelnick, Klaus; Herbert, Philip; Hinze, Michael
In: Control, optimisation and calculus of variations - Les Ulis: EDP Sciences, Bd. 28 (2022), 2, insges. 29 S.
Finite element error analysis for a system coupling surface evolution to diffusion on the surface
Deckelnick, Klaus; Styles, Vanessa
In: Interfaces and free boundaries - Zürich: European Mathematical Soc. Publ. House, Bd. 24 (2022), 1, S. 63-93
2021
Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces
Deckelnick, Klaus; Nürnberg, Robert
In: SIAM journal on numerical analysis/ Society for Industrial and Applied Mathematics - Philadelphia, Pa.: SIAM, Bd. 59 (2021), 5, S. 2698-2721
A practical phase field method for an elliptic surface PDE
Barrett, John W.; Deckelnick, Klaus; Styles, Vanessa
In: IMA journal of numerical analysis: IMAJNA/ Institute of Mathematics and Its Applications - Oxford: Oxford Univ. Press, Bd. 41 (2021), 3, S. 1668-1695
A novel p-harmonic descent approach applied to fluid dynamic shape optimization
Müller, Peter Marvin; Kühl, Niklas; Siebenborn, Martin; Deckelnick, Klaus; Hinze, Michael; Rung, Thomas
In: Structural and multidisciplinary optimization - Berlin: Springer, Bd. 64 (2021), 6, S. 3489-3503, 2017
A finite element error analysis for axisymmetric mean curvature flow
Barrett, John W.; Deckelnick, Klaus; Nürnberg, Robert
In: IMA journal of numerical analysis: IMAJNA/ Institute of Mathematics and Its Applications - Oxford: Oxford Univ. Press, Bd. 41 (2021), 3, S. 1641-1667
Boundary value problems for a special Helfrich functional for surfaces of revolution - existence and asymptotic behaviour
Deckelnick, Klaus; Doemeland, Marco; Grunau, Hans-Christoph
In: Calculus of variations and partial differential equations - Berlin: Springer, Bd. 60 (2021), insges. 31 S.
A novel finite element approximation of anisotropic curve shortening flow
Nürnberg, Robert; Deckelnick, Klaus
In: Magdeburg: Otto-von-Guericke-Universität, Fakultät für Mathematik, 2021, 31 Seiten, Diagramme - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2021, Nr. 2)
2020
Global minima for optimal control of the obstacle problem
Ali, Ahmad Ahmad; Deckelnick, Klaus; Hinze, Michael
In: Control, optimisation and calculus of variations: COCV - Les Ulis: EDP Sciences, Volume 26 (2020), articel 64, 22 Seiten
Error estimates for a finite difference approximation of mean curvature flow for surfaces of torus type
Mierswa, Alina; Deckelnick, Klaus
In: Magdeburg, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2020, 99 Seiten [Literaturverzeichnis: Seite 97-99][Literaturverzeichnis: Seite 97-99]
Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces
Deckelnick, Klaus; Nürnberg, Robert
In: Magdeburg: Universität, Fakultät für Mathematik, 2020, 24 Seiten - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2020, Nr. 06)
A practical phase field method for an elliptic surface PDE
Barrett, John W.; Styles, Vanessa; Deckelnick, Klaus
In: Magdeburg: Otto-von-Guericke-Universität, Fakultät für Mathematik, 2020, 24 Seiten - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2020, Nr. 03)
Boundary value problems for the Helfrich funtional for surfaces of revolution - existence and asymptotic behavior
Deckelnick, Klaus; Doemeland, Marco; Grunau, Hans-Christoph
In: Magdeburg: Universität, Fakultät für Mathematik, 2020, 29 Seiten, Diagramme - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2020, Nr. 04)
2019
Hamilton-Jacobi equations on an evolving surface
Deckelnick, Klaus; Elliott, Charles M.; Miura, Tatsu-Hiko; Styles, Vanessa
In: Mathematics of computation - Providence, RI: Soc., Bd. 88 (2019), 320, S. 2635-2664
Sufficient conditions for unique global solutions in optimal control of semilinear equations with C1 nonlinearity
Ahmad Ahmad, Ali; Deckelnick, Klaus; Hinze, Michael
In: Control and cybernetics / Systems Research Institute, Polish Academy of Sciences - Warszawa: SRI PAS, 1972, Bd. 2.2019, 2, S. 325-344
A finite element error analysis for axisymmetric mean curvature flow
Barrett, John W.; Deckelnick, Klaus; Nürnberg, Robert
In: SIAM journal on numerical analysis/ Society for Industrial and Applied Mathematics - Philadelphia, Pa.: SIAM . - 2019, 6, S. 2161-2179
Sufficient conditions for unique global solutions in optimal control of semilinear equations with C1-nonlinearity
Ali, Ahmad Ahmad; Deckelnick, Klaus; Hinze, Michael
In: Magdeburg: Universität, Fakultät für Mathematik, 2019, 18 Seiten, Diagramme - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2019,Nr.02)
A finite element error analysis for axisymmetric mean curvature flow
Barrett, John William; Nürnberg, Robert; Deckelnick, Klaus
In: Magdeburg: Otto-von-Guericke-Universität, Fakultät für Mathematik, 2019, 20 Seiten, Diagramme - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2019, Nr. 05)
2018
An obstacle problem for elastic graphs
Dall'Acqua, Anna; Deckelnick, Klaus
In: SIAM journal on mathematical analysis/ Society for Industrial and Applied Mathematics - Philadelphia, Pa.: SIAM, 1970, Bd. 50.2018, 1, S. 119-137
Error analysis for global minima of semilinear optimal control problems
Ahmad Ali, Ahmad; Deckelnick, Klaus; Hinze, Michael
In: Mathematical control and related fields: MCRF - Springfield, Mo.: AIMS, 2011, Bd. 8.2018, 1, S. 195-215
Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface
Deckelnick, Klaus; Styles, Vanessa
In: Numerische Mathematik - Berlin: Springer, 1959, Bd. 139.2018, 3, S. 709-741
Global minima for optimal control of the obstacle problem
Ali, Ahmad Ahmad; Deckelnick, Klaus; Hinze, Michael
In: Magdeburg: Universität, Fakultät für Mathematik, 2018, 22 Seiten, Diagramme - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2018,Nr.05)
2017
An optimal shape design problem for plates
Deckelnick, Klaus; Hinze, Michael; Jordan, Tobias
In: SIAM journal on numerical analysis - Philadelphia, Pa: SIAM, Bd. 55.2017, 1, S. 109-130
Minimising a relaxed Willmore functional for graphs subject to boundary conditions
Deckelnick, Klaus; Grunau, Hans-Christoph; Röger, Matthias
In: Interfaces and free boundaries - Zürich : European Mathematical Soc. Publ. House, Bd. 19.2017, 1, S. 109-140
Numerical analysis for a system coupling curve evolution to reaction diffusion on the curve
Barrett, John W.; Deckelnick, Klaus; Styles, Vanessa
In: SIAM journal on numerical analysis - Philadelphia, Pa: SIAM, Bd. 55.2017, 2, S. 1080-1100
Hamilton-Jacobi equations on an evolving surface
Deckelnick, Klaus; Elliott, Charles; Miura, Tatsu-Hiko
In: Magdeburg: Universität, Fakultät für Mathematik, 2017, 19 Seiten, Illustrationen - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2017,Nr.7)
An obstacle problem for elastic graphs*
Dall'Acqua, Anna; Deckelnick, Klaus
In: Magdeburg: Universität, Fakultät für Mathematik, 2017, 20 Seiten - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2017,Nr.02)
2016
Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa
In: Inverse problems: an international journal on the theory and practice of inverse problems, inverse methods and computerized inversion of data - Bristol [u.a.]: Inst., Vol. 32.2016, Art. 045008, insgesamt 26 S.
Global minima for semilinear optimal control problems
Ali, Ahmad Ahmad; Deckelnick, Klaus; Hinze, Michael
In: Computational optimization and applications : an international journal. - New York, NY [u.a.] : Springer Science + Business Media B.V, Bd. 65.2016, 1, S. 261-288
Numerical analysis for a system coupling curve evolution to reaction-diffusion on the curve
Barrett, John W.; Deckelnick, Klaus; Styles, Vanessa
In: Magdeburg: Universität, Fakultät für Mathematik, 2016, 20 Seiten, Diagramme - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2016,Nr.5)
Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface
Styles, Vanessa; Deckelnick, Klaus
In: Magdeburg: Universität, Fakultät für Mathematik, 2016, 26 Seiten - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2016,Nr.11)
2015
A C 1-finite element method for the Willmore flow of two-dimensional graphs
Deckelnick, Klaus; Katz, Jakob; Schieweck, Friedhelm
In: Mathematics of computation - Providence, RI: Soc, Bd. 84.2015, S. 2617-2643
An optimal shape design problem for plates
Hinze, Michael; Jordan, Tobias; Deckelnick, Klaus
In: Magdeburg, Univ., Fak. für Mathematik, 2015, 22 S., graph. Darst. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2015,11)
Minimising a relaxed Willmore functional for graphs subject to boundary conditions
Deckelnick, Klaus; Röger, Matthias; Grunau, Hans-Christoph
In: Magdeburg, Univ., Fak. für Mathematik, 2015, 29 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2015,6)
Global minima for semilinear optimal control problems
Ali, Ahmad; Hinze, Michael; Deckelnick, Klaus
In: Magdeburg, Univ., Fak. für Mathematik, 2015, 21 S., graph. Darst. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2015,8)
Double obstacle phase field approach to an inverse problem for a discontinuous diffusion coefficient
Elliot, Charles M.; Styles, Vanessa; Deckelnick, Klaus
In: Magdeburg, Univ., Fak. für Mathematik, 2015, 27 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2015,9)
2014
A-Priori error bounds for finite element approximation of elliptic optimal control problems with gradient constraints
Deckelnick, Klaus; Hinze, Michael
In: Trends in PDE Constrained Optimization - Cham : Birkhäuser/Springer ; Leugering, Günter . - 2014, S. 365-382 - (International Series of Numerical Mathematics; 165)
Unfitted finite element methods using bulk meshes for surface partial differential equations
Deckelnick, Klaus; Elliott, Charles M.; Ranner, Thomas
In: SIAM journal on numerical analysis - Philadelphia, Pa: SIAM, Bd. 52.2014, 4, S. 2137-2162
2013
Unstable Willmore surfaces of revolution subject to natural boundary conditions
DallAcqua, Anna; Deckelnick, Klaus; Wheeler, Glen
In: Calculus of variations and partial differential equations. - Berlin : Springer, Bd. 48.2013, 3/4, S. 293-313
A-priori error bounds for finite element approximation of elliptic optimal control problems with gradient constraints
Hinze, Michael; Deckelnick, Klaus
In: Magdeburg: Univ., Fak. für Mathematik, 2013, 15 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2013,14)
Unfitted finite element methods using bulk meshes for surface partial differential equations
Deckelnick, Klaus; Elliott, Charles M.; Ranner, Thomas
In: Magdeburg: Univ., Fak. für Mathematik, 2013, 26 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2013,29)
A C1-finite element method for the Willmore flow of two-dimensional graphs
Deckelnick, Klaus; Katz, Jakob; Schieweck, Friedhelm
In: Magdeburg: Univ., Fak. für Mathematik, 2013, 23 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2013,4)
2012
Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion
Barrett, John W.; Deckelnick, Klaus
In: Interfaces and free boundaries. - Zürich : European Mathematical Soc. Publ. House, Bd. 14.2012, 3, S. 343-363
A note on the approximation of elliptic control problems with bang-bang controls
Deckelnick, Klaus; Hinze, Michael
In: Computational optimization and applications - Norvell, Mass. : Springer, Bd. 51 (2012), Heft 2, S. 931-939
2011
Identification of matrix parameters in elliptic PDEs
Deckelnick, Klaus; Hinze, Michael
In: Control and cybernetics / Systems Research Institute, Polish Academy of Sciences - Warszawa : SRI PAS, Bd. 40.2011, 4, S. 957-970
Numerical analysis of an inverse problem for the eikonal equation
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa
In: Numerische Mathematik. - Berlin : Springer, Bd. 119.2011, 2, S. 245-269
Variational discretization of parabolic control problems in the presence of pointwise state constraints
Deckelnick, Klaus; Hinze, Michael
In: Journal of computational mathematics: an international journal on numerical methods, analysis and applications : an international journal on numerical methods, analysis and applications - Beijing : Chinese Acad. of Mathematics and System Sciences, Bd. 29.2011, 1, S. 1-15
2010
An h-narrow band finite-element method for elliptic equations on implicit surfaces
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.; Heine, Claus-Justus
In: IMA journal of numerical analysis . - Oxford : Oxford Univ. Press, Bd. 30.2010, 2, S. 351-376
Error analysis for the approximation of axisymmetric Willmore flow by C 1-finite elements
Deckelnick, Klaus; Schieweck, Friedhelm
In: Interfaces and free boundaries: modelling, analysis and computation / European Mathematical Society: modelling, analysis and computation - Zürich: European Mathematical Soc. Publ. House, Bd. 12 (2010), 4, S. 551-574
2009
Finite element approximation of dirichlet boundary control for elliptic PDEs on two- and three-dimensional curved domains
Deckelnick, Klaus; Günther, Andreas; Hinze, Michael
In: Society for Industrial and Applied Mathematics : SIAM journal on control and optimization . - Philadelphia, Pa. : Soc., Bd. 48.2009, 4, S. 2798-2819
Error analysis for the elastic flow of parametrized curves
Deckelnick, Klaus; Dziuk, Gerhard
In: Mathematics of computation . - Providence, RI : Soc., Bd. 78.2009, 266, S. 645-671
A Navier boundary value problem for Willmore surfaces of revolution
Deckelnick, Klaus; Grunau, Hans-Christoph
In: Analysis . - München : Oldenbourg, Bd. 29.2009, 3, S. 229-258
Stability and symmetry in the Navier problem for the one-dimensional Willmore equation
Deckelnick, Klaus; Grunau, Hans-Christoph
In: Society for Industrial and Applied Mathematics : SIAM journal on mathematical analysis . - Philadelphia, Pa. : SIAM, Bd. 40.2009, 5, S. 2055-1076
Finite element approximation of elliptic control problems with constraints on the gradient
Deckelnick, Klaus; Günther, Andreas; Hinze, Michael
In: Numerische Mathematik . - Berlin : Springer, Bd. 111.2009, 3, S. 335-350
Optimal control of the propagation of a graph in inhomogeneous media
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa
In: Society for Industrial and Applied Mathematics : SIAM journal on control and optimization . - Philadelphia, Pa. : Soc., Bd. 48.2009, 3, S. 1335-1352
2008
Numerical analysis of a control and state constrained elliptic control problem with piecewise constant control approximations
Deckelnick, Klaus; Hinze, Michael
In: Numerical mathematics and advanced applications . - Berlin [u.a.] : Springer, ISBN 3-540-69776-4, S. 597-604, 2008Kongress: ENUMATH 2007; (Graz) : 2007.09.10-14
Classical solutions to the dirichlet problem for Willmore surfaces of revolution
Dall'Acqua, Anna; Deckelnick, Klaus; Grunau, Hans-Christoph
In: Advances in calculus of variations. - Berlin : de Gruyter, Bd. 1.2008, 4, S. 379-397
2007
Convergence of a finite element approximation to a state-constrained elliptic control problem
Deckelnick, Klaus; Hinze, Michael
In: SIAM journal on numerical analysis: a publication of the Society for Industrial and Applied Mathematics/ Society for Industrial and Applied Mathematics - Philadelphia, Pa.: SIAM, Bd. 45 (2007), 5, S. 1937-1953
Existence, uniqueness and approximation of a doubly-degenerate nonlinear parabolic system modelling bacterial evolution
Barrett, John W.; Deckelnick, Klaus
In: Mathematical models & methods in applied sciences - Singapore [u.a.]: World Scientific, Bd. 17 (2007), 7, S. 1095-1127
Boundary value problems for the one-dimensional Willmore equation
Deckelnick, Klaus; Grunau, Hans-Christoph
In: Calculus of variations and partial differential equations - Berlin: Springer, Bd. 30 (2007), 3, S. 293-314
2006
Propagation of graphs in two-dimensional inhomogeneous media
Deckelnick, Klaus; Elliot, Charles M.
In: Applied numerical mathematics: transactions of IMACS - Amsterdam [u.a.]: Elsevier, Bd. 56 (2006), 9, S. 1163-1178
Error analysis of a finite element method for the Willmore flow of graphs
Deckelnick, Klaus; Dziuk, Gerhard
In: Interfaces and free boundaries - Zürich: European Mathematical Soc. Publ. House, Bd. 8 (2006), 1, S. 21-46
2005
Fully discrete finite element approximation for anisotropic surface diffusion of graphs.
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.
In: SIAM journal on numerical analysis [Philadelphia, Pa] 43(2005), Nr. 3, S. 1112 - 1138
Computation of geometric partial differential equations and mean curvature flow.
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles M.
In: Acta numerica [Cambridge] 4(2005), S. 139 - 232
2004
Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities.
Deckelnick, Klaus; Elliott, Charles M.
In: Interfaces and free boundaries [Zürich] 6(2004), S. 1 - 21
Semidiscretization and error estimates for distributed control of the instationary Navier- Stokes equations.
Deckelnick, Klaus; Hinze, Michael
In: Numerische Mathematik [Berlin] 97(2004), S. 297 - 320
2003
Mean curvature flow and related topics.
Deckelnick, Klaus; Dzink, Gerhard
In: Blowey, James F. (Hrsg.) ; ... (Hrsg.): Frontiers in numerical analysis. Berlin [u.a.] : Springer, 2003, S. 63 - 108
Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces.
Deckelnick, Klaus; Dziuk, Gerhard; Elliott, Charles
In: SIAM journal on numerical analysis [Philadelphia, Pa] 41(2003), Nr. 6, S. 2161 - 2179
Numerical approximation of mean curvature flow of graphs and level sets.
Deckelnick, Klaus; Dziuk, Gerhard
In: Ambrosio, Luigi (Verf.) ; ... (Verf.): Mathematical aspects of evolving interfaces : lectures given at the C.I.M.-C.I.M.E. joint Euro-Summer School held in Madeira, Funchal, Portugal, July 3 - 9, 2003. Berlin : Springer, 2003, S. 53 - 87 (Lecture notes in mathematics 1812, subseries: Fondazione CIME, Firenze)
Uniqueness and error bounds for eikonal equations with discontinuities.
Deckelnick, Klaus; Elliott, Charles
In: Ishii, H. (Hrsg.) ; Giga, Y. (Hrsg.) ; Koike, S. (Hrsg.): Viskosity solutions of differential equations and related topics (Conference held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, September 17-19, 2003). - proceedings. Kyoto : Univ., 2003, S. 37 - 44 (RIMS Kokyuroku 1323)