WiSe 18/19: Aufbaumodul: Numerik IV
Carsten Gräser
Comments
Content:
Geometric partial differential equations are describing the evolution ofand processes on surfaces. Geometric flows such as the now classical mean curvature flow, Willmore flow, and pdes on moving surfaces are typical examples. In this lecture, we will consider various formulations including phase field models of Allen-Cahn and Cahn-Hilliard type and concentrate on basic numerical techniques such as surface finite element methods, adaptivity,unfitted finite element methods, and efficient numerical solvers. Zielgruppe Advanced students in the Master Program Mathematics.Various possible topics for a Master thesis will come up during this course. Voraussetzungen Basic knowledge on partial differential equations and their numericalsolution (e.g. Numerik III).
Target audience:
This lecture is a continuation of the preceding course on "Numerical methods for partial differential equations (Numerik III)". It is intended to broaden the way towards a master thesis in the field of computational PDEs.
Prerequisites:
Participants should have some knowledge about PDEs and their numerical approximation by finite elements as provided, e.g., by the preceing course on "Numerical methods for partial differential equations (Numerik III)".
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closeSuggested reading
- Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)K.
- Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
- G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
- J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
- T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)
16 Class schedule
Regular appointments