相关论文: A posteriori estimates for the stochastic total va…

This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier Stokes equations with singular sources on Lipschitz, but not necessarily convex, polygonal domains. Under a…

The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…

Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in…

Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…

This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…

This paper investigates the pathwise uniform convergence in probability of fully discrete finite-element approximations for the two-dimensional stochastic Navier-Stokes equations with multiplicative noise, subject to no-slip boundary…

A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived {\it a posteriori} error estimator for…

This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…

In this paper we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming finite element method on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a new…

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…

In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg…

In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained in a Riemannian manifold. The difficulty of this problem is…

A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field…

We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated…