相关论文: Explicit k-dependency for $P_k$ finite elements in…

We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that…

This paper derives some discrete maximum principles for $P1$-conforming finite element approximations for quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial…

We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…

The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and…

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement…

The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…

Given the experimental precision in condensed matter physics -- positions are measured with errors of less than 0.1pm, energies with about 0.1meV, and temperature levels are below 20mK -- it can be inferred that standard quantum mechanics,…

We introduce a new weak Galerkin finite element method whose weak functions on interior neighboring edges are double-valued for parabolic problems. Based on $(P_k(T), P_{k}(e), RT_k(T))$ element, a fully discrete approach is formulated with…

We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…

Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…

In this paper, we derive quasi-optimal $\textit{a priori}$ error estimates for the kinematic pressure for a Finite Element (FE) approximation of steady systems of $p$-Navier-Stokes type in the case of shear-thickening, $\textit{i.e.}$, in…

We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time' and `length' scales is very explicit. Specialising to data…

The analysis of Tables of particle properties shows that the probability distribution of the results of physical measurements is far from the conventional Gaussian $\rho(\xi)=exp(-\xi^2/2) $, but is more likely to follow the simple…

After a recollection on compression through a projection onto a polyhedral set (which generalizes the compression by coordinates quantization), we express, in this framework, the probability that an image is coded with $K$ coefficients as…

We study discontinuous Galerkin approximations of the $p$--biharmonic equation from a variational perspective. We propose a discrete variational formulation of the problem based on a appropriate definition of a finite element Hessian and…

Numerous exact relations exist that relate the effective elastic properties of composites to the elastic properties of their components. These relations can not only be used to determine the properties of certain composites, but also…

Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of…

We prove an explicit finite-sample version of the Borel--Cantelli lemma under $m$-dependence. Given any $m$-dependent sequence of events $(A_k)_{1\leq k\leq N}$, we show that \[ \mathbb{P}\Bigl(\bigcup_{k=1}^N A_k\Bigr) \ge 1 -…

Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…