相关论文: On False Accuracy Verification of UMUSCL Scheme

In this work, we introduced a class of nonlocal models to accurately approximate the Poisson model on manifolds that are embedded in high dimensional Euclid spaces with Dirichlet boundary. In comparison to the existing nonlocal Poisson…

Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…

We present an exact first-order perturbation theory for the eigenmodes in systems with interfaces causing material discontinuities. We show that when interfaces deform, higher-order terms of the perturbation series can contribute to the…

Model checking is an automatic formal verification technique that is widely used in hardware verification. The state-of-the-art complete model-checking techniques, based on IC3/PDR and its general variant CAR, are based on computing…

In this article we present a refined convergence analysis for a second order accurate in time, fourth order finite difference numerical scheme for the 3-D Cahn-Hilliard equation, with an improved convergence constant. A modified backward…

Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…

We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…

Perturbation-based explanations are widely utilized to enhance the transparency of modern machine-learning models. However, their reliability is often compromised by the unknown model behavior under the specific perturbations used. This…

We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…

In weakly supervised learning, unbiased risk estimator(URE) is a powerful tool for training classifiers when training and test data are drawn from different distributions. Nevertheless, UREs lead to overfitting in many problem settings when…

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

In this paper we present the successive centralization of the circumcenter reflection scheme with several control sequences for solving the convex feasibility problem in Euclidean space. Assuming that a standard error bound holds, we prove…

A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…

The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…

In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327 ], Authors presented an algorithm (\textbf{Algorithm 2.3}) and stated…

In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy…

We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…

The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…

Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…

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…