相关论文: Residual estimates for post-processors in elliptic…

In a previous work, we introduced a discretization scheme for a constrained optimal control problem involving the fractional Laplacian. For such a control problem, we derived optimal a priori error estimates that demand the convexity of the…

With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed…

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…

This paper is concerned with a posteriori error bounds for linear transport equations and related questions of contriving corresponding adaptive solution strategies in the context of Discontinuous-Petrov-Galerkin schemes. After indicating…

We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…

In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…

A residual based {\em a posteriori} error estimator is derived for a quadratic finite element method (fem) for the elliptic obstacle problem. The error estimator involves various residuals consisting the data of the problem, discrete…

In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order…

We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…

In this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that the neural network solutions will converge if we increase…

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…

In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. The computation of estimators is simple once corresponding…

In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite element spaces, that are allowed to change in time. Our main…

We derive optimal and asymptotically exact a posteriori error estimates for the approximation of the Laplace eigenvalue problem. To do so, we combine two results from the literature. First, we use the hypercircle techniques developed for…

In this paper, we present a study of an a posteriori estimator for the discretization error of a non-standard finite difference scheme applied to boundary value problems defined on an infinite interval. In particular, we show how…

In this work, we propose an a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenvalues of elliptic operators. It is proven that the pointwise a…