The convergence rate of a multigrid method for the numerical solution of the Poisson equation on a uniform grid is estimated. The results are independent of the shape of the domain as long as it is convex and polygonal. On the other hand, pollution effects become apparent when the domain contains reentrant corners. To estimate the smoothing of the Gauss-Seidel relaxation, the smoothness is meas...

We propose a method to quantify the complexity of conditional probability measures by a Hilbert space seminorm of the logarithm of its density. The concept of Reproducing Kernel Hilbert Spaces (RKHS) is a flexible tool to define such a seminorm by choosing an appropriate kernel. We present several examples with artificial datasets where our kernel-based complexity measure is consistent with our...

We derive a framework for a posteriori error estimates in unsteady, nonlinear, possibly degenerate, advection-diffusion problems. Our estimators are based on a space-time equilibrated flux reconstruction and are locally computable. They are derived for the error measured in a space-time mesh-dependent dual norm stemming from the problem and meshes at hand augmented by a jump seminorm measuring ...

We describe a time-dependent functional involving the relative entropy and $\dot{H}^1$ seminorm, which decreases along solutions to spatially homogeneous Landau equation with Coulomb potential. The study of this monotone sheds light on competition between dissipation nonlinearity for equation. It enables us obtain new results concerning regularity/blowup issues