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GALERKIN AND RUNGE{KUTTA METHODS: UNIFIED FORMULATION, A POSTERIORI ERROR ESTIMATES AND NODAL SUPERCONVERGENCE
Continuous discontinuous Galerkin methods
2015/12/11
We unify the formulation and analysis of Galerkin and Runge{Kutta
methods for the time discretization of parabolic equations. This, together with
the concept of reconstruction of the approximate sol...
Optimal order a posteriori error estimates for a class of Runge{Kutta and Galerkin methods
error estimates Galerkin methods
2015/12/11
We derive a posteriori error estimates, which exhibit
optimal global order, for a class of time stepping methods of any
order that include Runge{Kutta Collocation (RK-C) methods and
the continuous ...
DIFFERENTIAL HARNACK ESTIMATES FOR TIME-DEPENDENT HEAT EQUATIONS WITH POTENTIALS
EQUATIONS WITH POTENTIALS DIFFERENTIAL HARNACK
2015/8/17
In this paper, we prove a differential Harnack inequality for positive
solutions of time-dependent heat equations with potentials. We also prove a gradient
estimate for the positive solution o...
Hypoelliptic estimates in radiative transfer.
Local pinching estimates in 3-dim Ricci flow
Local pinching estimates 3-dim Ricci flow Differential Geometry
2012/6/30
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on a...
Integral estimates for the trace of symmetric operators on complete submanifolds
Integral estimates trace of symmetric operators complete submanifolds Differential Geometry
2012/4/17
Let $\Phi:TM\to TM$ be a positive-semidefinite operator of class $C^1$ defined on a complete noncompact manifold $M$ isometrically immersed in a Hadamard space $\bar{M}$. In this paper, we given condi...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
Interior derivative estimates for the Kahler-Ricci flow
Interior derivative estimates the Kahler-Ricci flow Differential Geometry
2011/8/31
Abstract: We give a maximum principle proof of interior derivative estimates for the K\"ahler-Ricci flow, assuming local uniform bounds on the metric.
Basic Riemannian Geometry and Sobolev Estimates used in Symplectic Topology
Basic Riemannian Geometry Sobolev Estimates used Symplectic Topology
2011/2/22
This note collects a number of standard statements in Riemannian geometry and in Sobolevspace
theory that play a prominent role in analytic approaches to symplectic topology. These
include relations...
Approximate variances for tapered spectral estimates
Asymptotic variance data taper (smoothed) periodogram
2010/12/15
We propose an approximation of the asymptotic variance that removes a certain discontinuity in the formula for the raw and the smoothed periodogram in case a data taper is used. It is based on an appr...
Estimates for Fourier Transform of Measures Supported on Singular Hypersurfaces
Oscillatory Integrals oscillation index singular hypersurfaces curvature
2010/2/26
We consider hypersurfaces S \subset \RR3 with zero Gaussian curvature at every ordinary point with surface measure dS and define the surface measure dm = y(x)dS(x) for smooth function y with compact s...
