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Gerhard Dziuk
Abteilung für Angewandte Mathematik
Universität Freiburg
Hermann-Herder-Str.10
D-79104 Freiburg i. Br.
Tel. : 0761/203-5629
Fax : 0761/203-5632
Runge-Kutta time discretization of parabolic differential equations on evolving surfaces.
(with Ch. Lubich, D. Mansour)
Submitted (2010)
L2-estimates for the evolving surface finite element method.
(with C. M. Elliott)
Submitted (2010)
Theorie und Numerik partieller Differentialgleichungen.
Lehrbuch De Gruyter (2010)
An h-narrow band finite-element method for elliptic equations on implicit surfaces.
(with K. Deckelnick, C. M. Elliott, C.-J. Heine)
IMA J. Numer. Anal. 30, No. 2 (2010) 351-376. (online-Erstpublikation: 4. März 2009)
An Eulerian approach to transport and diffusion on evolving implicit surfaces.
(with C. M. Elliott)
Comput. Visual. Sci. 13, No. 1 (2010) 17-28. (online-Erstpublikation: 24. Juli 2008)
Error analysis for the elastic flow of parametrized curves.
(with K. Deckelnick)
Math. Comp. 78, No. 266 (2009) 645-671. (online-Erstpublikation: 17. Oktober 2008)
Computational parametric Willmore flow.
Numer. Math. 111, No. 1 (2008) 55-80. (online-Erstpublikation: 18. September 2008)
Eulerian finite element method for parabolic PDEs on implicit surfaces.
(with C. M. Elliott)
Interf. Free Bound. 10, No. 1 (2008) 119-138.
Surface finite elements for parabolic equations.
(with C. M. Elliott)
J. Comp. Math., Vol. 25, No. 4 (2007) 385-407. (online-Erstpublikation: 28. Mai 2007)
An adaptive finite element method for the Laplace-Beltrami operator on implicitly defined surfaces.
(with A. Demlow)
SIAM J. Numer. Anal. 45, No. 1 (2007) 421-442. (online-Erstpublikation: 15. Februar 2007)
Finite elements on evolving surfaces.
(with C. M. Elliott)
IMA J. Numer. Anal. 27, No. 2 (2007) 262-292. (online-Erstpublikation: 7. August 2006)
Finite elements on evolving surfaces.
(with C. M. Elliott)
Preprint, Fakultät für Mathematik und Physik, Universität Freiburg Nr. 05-11 (2005)
Computation of geometric partial differential equations and mean curvature flow.
(with K. Deckelnick, C. M. Elliott)
Acta Numerica 14 (2005) 139-232. (online-Erstpublikation: 19. April 2005)
Error analysis of a finite element method for the Willmore flow of graphs. (Correction to this paper)
(with K. Deckelnick)
Interf. Free Bound. 8, No. 1 (2006) 21–46.
Error estimates for the Willmore flow of graphs.
(with K. Deckelnick)
Preprint, Fakultät für Mathematik und Physik, Universität Freiburg Nr. 25-04 (2004)
A finite element level set method for anisotropic mean curvature flow with space dependent weight.
(with K. Deckelnick)
in: S. Hildebrandt, H. Karcher (Hrsg.): Geometric Analysis and Nonlinear Partial Differential Equations. Springer : Berlin-Heidelberg-New York (2003) 249-264.
A finite element method for surface restoration with smooth boundary conditions.
(with U. Clarenz, U. Diewald, M. Rumpf, R. Rusu)
Comp. Aid. Geom. Des. 21, No. 5 (2004) 427-445. (online-Erstpublikation: 19. März 2004)
On generalized mean curvature flow in surface processing.
(with U. Clarenz, M. Rumpf)
in: S. Hildebrandt, H. Karcher (Hrsg.): Geometric Analysis and Nonlinear Partial Differential Equations. Springer : Berlin-Heidelberg-New York (2003) 217-248.
Fully discrete semi-implicit second order splitting for anisotropic surface diffusion of graphs.
(with K. Deckelnick, C.M. Elliott)
SIAM J. Numer. Anal. 43, No. 3 (2005) 1112-1138.
Finite element approximations to surfaces of prescribed variable mean curvature.
(with J. E. Hutchinson)
Numerische Mathematik 102, No. 4 (2006) 611-648. (online-Erstpublikation: 17. Dezember 2005)
Finite element approximations to surfaces of prescribed variable mean curvature.
(with J. E. Hutchinson)
Preprint, Fakultät für Mathematik und Physik, Universität Freiburg Nr. 03-01 (2003)
Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow.
(with K. Deckelnick)
in: M. Falcone, C. Makridakis (eds.): Numerical Methods for Viscosity Solutions and Applications. World Scientific Publ.: Singapore u.a. (2001) = Series Adv. Math. Appl. Sciences 59 (2001) 77-93.
Numerical approximations of mean curvature flow of graphs and level sets.
(with K. Deckelnick)
In: L. Ambrosio, K. Deckelnick, G. Dziuk, M. Mimura, V. A. Solonnikov, H. M. Soner (eds): Mathematical aspects of evolving interfaces. Springer : Berlin-Heidelberg-New York (2003) = Lecture Notes in Mathematics 1812 (2003) 53-87.
Error analysis of a semidiscrete numerical scheme for diffusion in axially symmetric surfaces.
(with K. Deckelnick, C. M. Elliott)
SIAM J. Numer. Anal. 41, No. 6 (2003) 2161-2179.
Evolution of elastic curves in Rn : Existence and computation.
(with E. Kuwert, R. Schätzle).
SIAM J. Math. Anal. 33, No. 5 (2003) 1228-1245.
A fully discrete numerical scheme for weighted mean curvature flow.
(with K. Deckelnick).
Numer. Math. 91, No.3 (2002) 423-452.
Mean curvature flow and related topics.
(with K. Deckelnick)
in: Blowey, J. F.; Craig, A.W.; Shardlow, T. (eds.): Frontiers in numerical analysis. 10th LMS-EPSRC numerical analysis summer school, Durham, UK, July 7-19, 2002. Springer : Berlin-Heidelberg New York (2003) = Universitext (2003) 63-108.
Mean curvature flow and related topics
Preprint, Fakultät für Mathematik und Physik, Universität Freiburg Nr. 02-33 (2002)
Discrete anisotropic curve shortening flow.
SIAM J. Numer. Anal. 36, No.6 (1999) 1808-1830.
The discrete Plateau Problem: Convergence results.
(with J. E. Hutchinson)
Mathematics of Computation 68, No.226 (1999) 519-546.
The discrete Plateau Problem: Algorithm and numerics.
(with J. E. Hutchinson)
Mathematics of Computation 68, No.225 (1999) 1-23.
Discrete anisotropic curvature flow of graphs.
with K. Deckelnick)
Mathematical Modelling and Numerical Analysis 33, No. 6 (1999) 1203-1222.
On the approximation of unstable minimal surfaces.
(with J. E. Hutchinson)
Calculus of Variations and Partial Differential Equations 4, No. 1 (1996) 27-58.
Convergence of a finite element method for non-parametric mean curvature flow.
(with K. Deckelnick)
Numerische Mathematik 72, No.2 (1995) 197-222.
Convergence of a semi-discrete scheme for the curve shortening flow.
Mathematical Models and Methods in Applied Sciences 4, No. 4 (1994) 589-606.
An algorithm for evolutionary surfaces.
Numerische Mathematik 58, No. 1 (1991) 603-611.
Finite Elements for the Beltrami operator on arbitrary surfaces.
In: S. Hildebrandt, R. Leis (eds.): Partial differential equations and calculus of variations. Springer : Berlin-Heidelberg-New York-London-Paris-Tokyo (1988) = Lecture Notes in Mathematics 1357 (1988) 142-155.
C2-Regularity for partially free minimal surfaces.
Mathematische Zeitschrift 189, No. 1 (1985) 71-79.
