scholarly journals Sharp stability of Brunn–Minkowski for homothetic regions

2021 ◽  
Author(s):  
Peter van Hintum ◽  
Hunter Spink ◽  
Marius Tiba
Keyword(s):  
Sharp Stability

scholarly journals A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN

2011 ◽  
Vol 21 (12) ◽  
pp. 2491-2521 ◽  
Author(s):  
CHRISTOPH ORTNER ◽  
HAO WANG
Keyword(s):  
Error Estimates ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Stability Estimates ◽  
Norm Estimates ◽  
Priori Error Estimates ◽  
Sharp Stability ◽  
Consistency Error ◽  
Periodic Chain ◽  
Homogeneous Strain

We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasi-nonlocal QC method. Our analysis decomposes the consistency error into modeling and coarsening errors. While previous results on estimating the modeling error exist, we present a new and simpler proof based on negative-norm estimates. Our stability analysis extends previous results on sharp stability estimates under homogeneous strain to the nonlinear setting. Finally, we present numerical experiments to illustrate the results of our analysis.

scholarly journals Sharp stability results for almost conformal maps in even dimensions

1999 ◽  
Vol 9 (4) ◽  
pp. 671-681 ◽  
Author(s):  
Stefan Müller ◽  
Vladimir Šverák ◽  
Baisheng Yan
Keyword(s):  
Conformal Maps ◽  
Sharp Stability ◽  
Stability Results

scholarly journals On a Novel Numerical Scheme for Riesz Fractional Partial Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2014
Author(s):  
Junjiang Lai ◽  
Hongyu Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
A Priori ◽  
Time Derivative ◽  
Stability Estimates ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Sharp Stability

In this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose a Galerkin finite element scheme for both the temporal and spatial discretizations. For the proposed numerical scheme, we derive sharp stability estimates as well as optimal a priori error estimates. Extensive numerical experiments are conducted to verify the promising features of the newly proposed method.

Analysis of Geometrically Consistent Schemes with Finite Range Interaction

2017 ◽  
Vol 22 (5) ◽  
pp. 1333-1361
Author(s):  
Hongliang Li ◽  
Pingbing Ming
Keyword(s):  
Error Estimate ◽  
Numerical Experiments ◽  
Optimal Error Estimate ◽  
Finite Range ◽  
Dimensional Problem ◽  
Optimal Error ◽  
Range Interaction ◽  
One Dimensional ◽  
Sharp Stability ◽  
Theoretical Results

AbstractWe analyze the geometrically consistent schemes proposed by E. Lu and Yang [6] for one-dimensional problem with finite range interaction. The existence of the reconstruction coefficients is proved, and optimal error estimate is derived under sharp stability condition. Numerical experiments are performed to confirm the theoretical results.

scholarly journals Sharp Stability of Some Spectral Inequalities

2012 ◽  
Vol 22 (1) ◽  
pp. 107-135 ◽  
Author(s):  
Lorenzo Brasco ◽  
Aldo Pratelli
Keyword(s):  
Sharp Stability

scholarly journals High order numerical schemes for transport equations on bounded domains

2021 ◽  
Vol 70 ◽  
pp. 84-106
Author(s):  
B. Boutin ◽  
T.H.T. Nguyen ◽  
A. Sylla ◽  
S. Tran-Tien ◽  
J.-F. Coulombel
Keyword(s):  
Boundary Data ◽  
Convergence Rates ◽  
Summer Camp ◽  
Stability Estimates ◽  
Bounded Domains ◽  
Finite Difference Approximations ◽  
Gravity Flows ◽  
Optimal Convergence Rates ◽  
Sharp Stability ◽  
Geophysical Fluids

This article is an account of the NABUCO project achieved during the summer camp CEMRACS 2019 devoted to geophysical fluids and gravity flows. The goal is to construct finite difference approximations of the transport equation with nonzero incoming boundary data that achieve the best possible convergence rate in the maximum norm. We construct, implement and analyze the so-called inverse Lax-Wendroff procedure at the incoming boundary. Optimal convergence rates are obtained by combining sharp stability estimates for extrapolation boundary conditions with numerical boundary layer expansions. We illustrate the results with the Lax-Wendroff and O3 schemes.

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