Mini Symposium on Numerical Analysis of Nonlinear Evolution Equations
Organiser: Endre Suli
Thursday 2 July 2009
John W. W. Barrett (Imperial College)
Sören Bartels (Bonn) Robust approximation of phase field models past topological changes
Phase field models are often used to describe the evolution ofsubmanifolds, e.g., the Allen-Cahn equation approximates motion by meancurvature and more sophisticated phase field models provideregularizations of Willmore flow and other geometric evolution problems.The models involve small regularization parameters and we discuss thedependence of a priori and a posteriori error estimates for thenumerical solution of the regularized problems on this parameter. Inparticular, we address the question whether robust error estimation ispossible past topological changes. We provide an affirmative answer fora priori error estimates assuming a logarithmic scaling law of the timeaveraged principal eigenvalue of the linearized Allen-Cahn orGinzburg-Landau operator. This scaling law is confirmed by numericalexperiments for generic topological changes. The averaged eigenvalueenters a posteriori error estimates exponentially and therefore,critical scenarios are detected automatically by related adaptive finiteelement methods.
Charlie Elliott (Warwick) Computational Evolutionary PDEs on Surfaces
Evolutionary PDEs on stationary and moving surfaces appear in many applications such as the diffusion of surfactants on fluid interfaces, surface pattern formation on growing domains, segmentation on curved surfaces and phase separation on biomembranes and dissolving alloy surfaces. In this talk I discuss recent work with G. Dziuk (Freiburg) on novel finite element methods on triangulated surfaces and implicit surfaces defined as level sets.
Endre Suli (Oxford) Analysis and approximation of coupled Navier-Stokes-Fokker-Planck systems in kinetic models of dilute polymers
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