Computation of geometric partial differential equations and mean curvature flow

By Klaus Deckelnick, Gerhard Dziuk, Charles M. Elliott. Acta Numerica, 2005

481 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ab60bbc32fc142f340be8ca30b93af3031c50667

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute (2011, background): “[1] for details in the continuous case.”
Numerical approximation of gradient flows for closed curves in Rd (2010, methodology): “For readers not familiar with numerical methods for geometric evolution equations, we refer to Deckelnick, Dziuk, and Elliott (2005) for a recent overview.”
Geodesic finite elements on simplicial grids (2012, background): “We will now use these geodesic finite elements to solve PDEs for functions inH 1.”
A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes (2015, unknown): “Then the normal velocity in (x0, t0) is given by V(x0, t0) = d dt ∣∣∣ t0 γt(s0) · νγ(x0, t0), see also [11].”
Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities (2011, background): “In order to derive a free energy inequality for the sharp interface limit we need the following transport identities, for a proof see [10].”
Finite element analysis for a coupled bulk-surface partial differential equation (2013, methodology): “Derivation of variational form 2.1 Surface properties Throughout we will use the notation from Deckelnick et al. (2005).”
Geometric flows with rough initial data (2009, background): “For results on this flow see for example [7].”
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints (2010, methodology): “[18], for solution methods for fully implicit time discretizations of the Allen–Cahn equation.”
Finite element methods for surface PDEs* (2013, methodology): “These arise in phase field approximations of interface problems (Caginalp 1989, Deckelnick et al. 2005), and it is natural to exploit the methodology to generate methods for solving partial differential equations on the interfaces (Rätz and Voigt 2006, Elliott, Stinner, Styles and Welford 2011).”