Develops auxiliary gradient-flow solvers that shift nonlinearity in N-function governed variational problems to an auxiliary variable, with metric-space convergence proofs for p-Laplacian and p-Stokes in 4/3 ≤ p ≤ 4 and practical discretizations outperforming Newton in tests.
Lecture Notes on Gradient Flows and Optimal Transport
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abstract
We present a short overview on the strongest variational formulation for gradient flows of geodesically $\lambda$-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.
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Auxiliary Gradient-Flow Solvers for Generalized Newtonian Models
Develops auxiliary gradient-flow solvers that shift nonlinearity in N-function governed variational problems to an auxiliary variable, with metric-space convergence proofs for p-Laplacian and p-Stokes in 4/3 ≤ p ≤ 4 and practical discretizations outperforming Newton in tests.