Related papers: Maximum-norm a posteriori error bounds for an extr…
We consider the reaction diffusion problem and present efficient ways to discretize and precondition in the singular perturbed case when the reaction term dominates the equation. Using the concepts of optimal test norm and saddle point…
This work investigates the optimal error estimate of the fully discrete scheme for the variable-exponent subdiffusion model under the nonuniform temporal mesh. We apply the perturbation method to reformulate the original model into its…
In this article, a parameter-uniform numerical method is presented to solve one-dimensional singularly perturbed parabolic convection-diffusion turning point problem exhibiting two exponential boundary layers. We study the asymptotic…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…
Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…
This work is motivated by the need of efficient numerical simulations of gas flows in the serpentine channels used in proton-exchange membrane fuel cells. In particular, we consider the Poisson problem in a 2D domain composed of several…
This contribution introduces a novel signal extrapolation algorithm and its application to image error concealment. The signal extrapolation is carried out by iteratively generating a model of the signal suffering from distortion. Thereby,…
In this article, we study a two-dimensional singularly perturbed parabolic equation of the convection-diffusion type, characterized by discontinuities in the source term and convection coefficient at a specific point in the domain. These…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Frikha2013]. This allows us to extend and develop the Richardson-Romberg extrapolation method…
We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the…
We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems. The error bound is obtained from…
In this study, we employ the variational multiscale (VMS) concept to develop a posteriori error estimates for the stationary convection-diffusion-reaction equation. The variational multiscale method is based on splitting the continuous part…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
This paper contains construction and analysis a finite element approximation for convection dominated diffusion problems with full coefficient matrix on general simplicial partitions in $R^d$, $d=2,3$. This construction is quite close to…
Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…
In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…