Related papers: Practical Error Estimates for Reynolds' Lubricatio…
Lubrication problems at lengthscales for which the traditional Navier-Stokes description fails can be solved using a modified Reynolds lubrication equation that is based on the following two observations: first, classical Reynolds equation…
The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysis-of-variance dimensional…
We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions…
This paper is dedicated to the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the highly oscillatory regime. We compute an approximate solution based on the well-known WKB-ansatz, which relies on…
The truncation and approximation errors for the set of numerical solutions computed by methods based on the algorithms of different structure are calculated and analyzed for the case of the two-dimensional steady inviscid compressible flow.…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method and a second-order projection method along the trajectories of the…
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…
Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation -- a…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
Motivated by lubrication problems, we consider a micropolar uid ow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < " << 1. We prove the existence and uniqueness of a…
We study the approximation error $\varepsilon(x)=\operatorname{li}_{*}(x)-\operatorname{li}(x)$ arising from the classical Stieltjes asymptotic expansion for the logarithmic integral. Our analysis is based on the discrete values…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
In this work we develop and analyze a Reynolds-semi-robust and pressure-robust Hybrid High-Order (HHO) discretization of the incompressible Navier--Stokes equations. Reynolds-semi-robustness refers to the fact that, under suitable…
In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is large enough. This means that the accuracy that can be reached…
The energy method, also known as the Reynolds-Orr equation, is widely utilized in predicting the unconditional stability threshold of shear flows owing to the zero contribution of nonlinear terms to the time derivative of perturbation…
The role of the operator-product expansion in QCD calculations is discussed. Approximating the two-point correlation function by several terms and assuming an upper bound on the truncation error along the euclidean ray, we consider two…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…