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Homepage von Prof. Dr. Gerhard Dziuk |
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Gerhard Dziuk
Abteilung für Angewandte Mathematik Universität Freiburg Hermann-Herder-Str.10 D-79104 Freiburg i. Br. Tel. :
0761/203-5628 (5629)
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Projekte der Arbeitsgruppe |
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Lebenslauf |
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Lehre |
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| Recent Publications | |
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Error analysis for the elastic flow of parametrized curves. (with K. Deckelnick) Preprint Fakultät für Mathematik und Physik, Universität Freiburg Nr. 14-07 (2007) |
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Computational parametric Willmore flow. Numer. Math. No. 111, 55-80 (2008) |
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An Eulerian level set method for partial differential equations on evolving surfaces. (with C. M. Elliott) To appear in Comp. Viz. Sc., Preprint Fakultät für Mathematik und Physik, Universität Freiburg, Nr. 09-07 (2007) |
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Eulerian finite element method for parabolic PDEs on implicit surfaces. (with C. M. Elliott) Interf. Free Bound. 10 (2008) 119-138 |
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Surface finite elements for parabolic equations. (with C. M. Elliott) J. Comp. Math., Vol. 25, No. 4 (2007) 385-407 |
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Finite elements on evolving surfaces. (with C. M. Elliott) IMA J. Numer. Anal. 27, No. 2 (2006) 262-292 |
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Computation of geometric partial differential equations and mean curvature flow. (with K. Deckelnick, C. M. Elliott) Acta Numerica (2005), pp. 139-232 |
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Error analysis of a finite element method for the Willmore flow of graphs. (with K. Deckelnick) Interf. Free Bound. 8, No. 1 (2006) 21-46 |
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A finite element level set method for anisotropic mean curvature flow with space dependent weight. (with K. Deckelnick) in Geometric Analysis and Nonlinear Partial Differential Equations (S. Hildebrandt, H. Karc her, Hrsg.), 249-264, Springer, Berlin-Heidelberg-New York (2003) |
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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 (2004), 427-445 |
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On generalized mean curvature flow in surface processing. (with U. Clarenz, M. Rumpf) in Geometric Analysis and Nonlinear Partial Differential Equations (S. Hildebrandt, H. Karcher, Hrsg.), 217-248, Springer, Berlin-Heidelberg-New York (2003) |
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| Fully discrete semi-implicit second order splitting for anisotropic
surface diffusion of graphs. (with K. Deckelnick, C.M. Elliott) SIAM Journal on Numerical Analysis 43, (2005) 1112-1138 |
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Finite element approximations to surfaces of prescribed variable mean curvature. (with J. E. Hutchinson) Numerische Mathematik 102 (2006) 611-648 |
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| Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow.
(with K. Deckelnick) in Numerical methods for Viscosity Solutions and Applications. (M. Falcone, C. Makridakis eds.), 77-93, Series Adv. Math. Appl. Sciences 59 (2001) |
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Numerical approximations of mean curvature flow of graphs and level sets.
(with K. Deckelnick) in Mathematical aspects of evolving interfaces. (L. Ambrosio, K. Deckelnick, G. Dziuk, M. Mimura, V. A. Solonnikov, H. M. Soner, eds.) 53-87, Springer, Berlin-Heidelberg-New York (2003) |
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| Selected Publications | |
| Error analysis of a semidiscrete numerical scheme for diffusion
in axially symmetric surfaces. (with K. Deckelnick, C. M. Elliott) SIAM J. Numer. Anal. Vol 41, No. 6, 2161-2179 (2003) |
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| Evolution of elastic curves in Rn : Existence and computation. (with E. Kuwert, R. Schätzle). SIAM J. Math. Anal. Vol. 33, No. 5, 1228-1245 (2002) |
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| A fully discrete numerical scheme for weighted mean curvature
flow . (with K. Deckelnick). Numer. Math. 91, No.3, 423-452 (2002) |
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| Mean curvature flow and related topics. (with K. Deckelnick) in: Blowey, J. F. (ed.) et al., Frontiers in numerical analysis. 10th LMS-EPSRC numerical analysis summer school, Durham, UK, July 7-19, 2002. Berlin: Springer. Universitext 63-108 (2003). Preprint Fakultät für Mathematik und Physik, Universität Freiburg Nr. 02-33 (2002) |
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| Discrete anisotropic curve shortening flow. SIAM Numer. Anal. 36, Nr. 6, pp. 1808-1830 (1999) |
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| The discrete Plateau Problem: Convergence results. (with J. E. Hutchinson) Mathematics of Computation 68, pp. 519-546 (1999) |
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| The discrete Plateau Problem: Algorithm and numerics. (with J. E. Hutchinson), Mathematics of Computation 68, 1-23 (1999). |
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| Discrete anisotropic curvature flow of graphs. (with K. Deckelnick) Mathematical Modelling and Numerical Analysis - RAIRO 33, Nr. 6, pp. 1203-1222 (1999) |
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| On the approximation of unstable minimal surfaces, (with J. E. Hutchinson) Calculus of Variations and Partial Differential Equations 4, 27-58 (1995). |
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| Convergence of a finite element method for non-parametric mean curvature flow. (with K. Deckelnick) Numerische Mathematik 72, 197-222 (1995). |
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| Convergence of a semi-discrete scheme for the curve shortening flow. Mathematical Models and Methods in Applied Sciences 4, No. 4 (1994), 589-606. |
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| An algorithm for evolutionary surfaces. Numerische Mathematik 58, 603-611 (1991). |
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| Finite Elements for the Beltrami operator on arbitrary surfaces. In: S. Hildebrandt, R. Leis (Herausgeber): Partial differential equations and calculus of variations. Lecture Notes in Mathematics 1357, Springer Berlin Heidelberg New York London Paris Tokyo 1988, 142-155. |
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| C2-Regularity for partially free minimal surfaces. Mathematische Zeitschrift 189, 71-79 (1985). |
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