Related papers: Optimal finite-differences discretization for the …
Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward…
We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
For a model convection-diffusion problem, we obtain new error estimates for a general upwinding finite element discretization based on bubble modification of the test space. The key analysis tool is based on finding representations of the…
We compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a…
In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are established in the case of three dimensional polyhedral and…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
This paper provides a finite difference discretization for the backward Feynman-Kac equation, governing the distribution of functionals of the path for a particle undergoing both reaction and diffusion [Hou and Deng, J. Phys. A: Math.…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…