Related papers: Goal-oriented error estimation and adaptivity in M…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…
In this paper, we propose a novel iterative multiscale framework for solving high-contrast contact problems of Signorini type. The method integrates the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM)…
We consider a variant of the conventional MsFEM approach with enrichments based on Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A convergence analysis of the approach is presented. Residue-type a…
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,…
This work is concerned with the rigorous analysis on the Generalized Multiscale Finite Element Methods (GMsFEMs) for elliptic problems with high-contrast heterogeneous coefficients. GMsFEMs are popular numerical methods for solving flow…
Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To…
In this paper, a constructive and systematic strategy with more apparent degrees of freedom to achieve the accurate estimation of unknown parameters via a control perspective is proposed. By adding a virtual control in the final equation of…
In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…
Simulating flow in a highly heterogeneous reservoir with multiscale characteristics could be considerably demanding. To tackle this problem, we propose a numerical scheme coupling the Generalized Multiscale Finite Element Method (GMsFEM)…
Concept relatedness estimation (CRE) aims to determine whether two given concepts are related. Existing methods only consider the pairwise relationship between concepts, while overlooking the higher-order relationship that could be encoded…
Error mitigation techniques, while instrumental in extending the capabilities of near-term quantum computers, often suffer from exponential resource scaling with noise levels. To address this limitation, we introduce a novel approach,…
In this paper, the adaptive numerical solution of a 2D Poisson model problem by Crouzeix-Raviart elements ($\operatorname*{CR}_{k}$ $\operatorname*{FEM}$) of arbitrary odd degree $k\geq1$ is investigated. The analysis is based on an…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes…
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…
We present a wide-reaching revamp of the generalized many-body expanded full configuration interaction (MBE-FCI) method. First, we outline how to automatize the selection of reference active spaces whereby the inherent bias introduced…
Measurement error in count data is common but underexplored in the literature, particularly in contexts where observed scores are bounded and arise from discrete scoring processes. Motivated by applications in oral reading fluency…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
Classifiers are often utilized in time-constrained settings where labels must be assigned to inputs quickly. To address these scenarios, budgeted multi-stage classifiers (MSC) process inputs through a sequence of partial feature acquisition…
The intrinsic capability to continuously learn a changing data stream is a desideratum of deep neural networks (DNNs). However, current DNNs suffer from catastrophic forgetting, which interferes with remembering past knowledge. To mitigate…