Related papers: Optimal estimation for the Fujino-Morley interpola…
A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all…
This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities. These results have been obtained in…
We study $W^{1,p}$ Lagrange interpolation error estimates for general quadrilateral $\mathcal{Q}_{k}$ finite elements with $k\ge 2$. For the most standard case of $p=2$ it turns out that the constant $C$ involved in the error estimate can…
We establish new Euclidean Sobolev logarithmic inequalities in the framework of fractional Sobolev spaces and their weighted version. Our approach relies on a interpolation inequality, which can be viewed as a fractional…
A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed guaranteed computation methods for both eigenvalues and…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the current literature, we show that the Lebesgue constant of…
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the…
We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator that estimates vectors from with a controlled associated…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the…
We derive a residual-based $hp$-a posteriori error estimator for hybrid high-order (HHO) methods on simplicial meshes applied to the biharmonic problem posed on two- and three-dimensional polytopal Lipschitz domains. The a posteriori error…
A method to retrieve the elastic constants of rectangular wooden plates is presented, relying on the measurement of a set of eigenfrequencies and the identification of the corresponding mode shapes, and belonging to the more general…
We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which…
A new alternative numerical procedure to the Szeg\H{o} quadrature formulas for the estimation of integrals with respect to a positive Borel measure $\mu$ supported on the unit circle is presented. As in many practical situations, we assume…