Related papers: Thin obstacle problem: estimates of the distance t…
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…
Computing the distance function to some surface or line is a problem that occurs very frequently. There are several ways of computing a relevant approximation of this function, using for example technique originating from the approximation…
We derive guaranteed bounds of distance to the exact solution of the evolutionary reaction-diffusion problem with mixed Dirichlet-Neumann boundary condition. It is shown that two-sided error estimates are directly computable and equivalent…
We derive a new residual-type a posteriori estimator for a singularly perturbed reaction-diffusion problem with obstacle constraints. It generalizes robust residual estimators for unconstrained singularly perturbed equations. Upper and…
We consider the obstacle problem with irregular barriers for semilinear elliptic equation involving measure data and operator corresponding to a general quasi-regular Dirichlet form. We prove existence and uniqueness of a solution as well…
We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determined by a single measurement of displacement and normal stress…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral…
In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solution is uniquely determined. How to incorporate obstacles,…
We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback-Leibler divergence, we show that the Wasserstein distance provides…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
We consider the numerical approximation of variational problems with orthotropic growth, that is those where the integrand depends strongly on the coordinate directions with possibly different growth in each direction. Under realistic…
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…
In this note, we concentrate on the backward error of the equality constrained indefinite least squares problem. For the normwise backward error of the equality constrained indefinite least square problem, we adopt the linearization method…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
This paper investigates elliptic obstacle problems with generalized Orlicz growth involving measure data, which includes Orlicz growth, variable exponent growth, and double-phase growth as specific cases of this setting. First, we establish…