Related papers: A Posteriori Error Estimates for Nonconforming App…
The paper is concerned with functional type a posteriori estimates for the initial boundary value problem for a parabolic partial differential equation with an obstacle. We deduce a guaranteed and computable bound of the distance between…
First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new Kuznetsov type theory and obtain general and possibly optimal…
We derive a posteriori error estimates for the hybridizable discontinuous Galerkin (HDG) methods, including both the primal and mixed formulations, for the approximation of a linear second-order elliptic problem on conforming simplicial…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
Simulations are made of a probe particle diffusing through a complex fluid. Probe particle motions are described by the Mori-Zwanzig equation and Mori's orthogonal hierarchy of random forces scheme, subject to the approximation that the…
The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
Solutions of an optimization problem are sensitive to changes caused by approximations or parametric perturbations, especially in the nonconvex setting. This paper shows that solutions of substitute problems, constructed from Rockafellian…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately solved via Gaussian filtering and smoothing, whenever a…
We present reliable a-posteriori error estimates for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems. Starting from our earlier work on $h$ adaptive finite element approximations we show a way to obtain…