相关论文: On False Accuracy Verification of UMUSCL Scheme

We explore the effects of three-loop minimal supersymmetric standard model renormalisation group equation terms and some leading two-loopthreshold corrections on gauge and Yukawa unification: each being one loop higher order than current…

We discuss the order, efficiency, stability and positivity of several meshless schemes for linear scalar hyperbolic equations. Meshless schemes are Generalised Finite Difference Methods (GFDMs) for arbitrary irregular grids in which there…

In electromagnetic simulations of magnets and machines one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is…

The model uncertainty obtained by variational Bayesian inference with Monte Carlo dropout is prone to miscalibration. In this paper, different logit scaling methods are extended to dropout variational inference to recalibrate model…

In [Kopteva, Math. Comp., 2014] a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is…

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…

Scale-separated AdS compactifications of string theory can be constructed at the two-derivative supergravity level in the presence of smeared orientifold planes. The unsmearing corrections are known to leading order in the large volume,…

Higher-order modal fixpoint logic (HFL) is a higher-order extension of the modal mu-calculus, and strictly more expressive than the modal mu-calculus. It has recently been shown that various program verification problems can naturally be…

The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…

Last-layer retraining (LLR) methods -- wherein the last layer of a neural network is reinitialized and retrained on a held-out set following ERM training -- have garnered interest as an efficient approach to rectify dependence on spurious…

In this paper we present a formally fourth-order accurate hybrid-variable method for the Euler equations in the context of method of lines. The hybrid-variable (HV) method seeks numerical approximations to both cell-averages and nodal…

In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5,9]. However, one may wonder if this…

It is well known that the Euler method for a random ordinary differential equation $\mathrm{d}X_t/\mathrm{d}t = f(t, X_t, Y_t)$ driven by a stochastic process $\{Y_t\}_t$ with $\theta$-H\"older sample paths is estimated to be of strong…

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. We consider a new unfitted finite element method…

We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…

The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…

The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate…

The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easily constructed and relatively uncomplicated to investigate…

In the present paper, superconvergence of second order, after an appropriate postprocessing, is achieved for both the two and three dimensional first order rectangular Morley elements of biharmonic equations. The analysis is dependent on…