相关论文: Superconvergent Gradient Recovery for Virtual Elem…

One remarkable feature of virtual element methods (VEMs) is their great flexibility and robustness when used on almost arbitrary polytopal meshes. This very feature makes it widely used in both fitted and unfitted mesh methods. Despite…

In the present paper we develop the Virtual Element Method for hyperbolic problems on polygonal meshes, considering the linear wave equations as our model problem. After presenting the semi-discrete scheme, we derive the convergence…

This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…

Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…

The proximal Galerkin (PG) method is a finite element method for solving variational problems with inequality constraints. It has several advantages, including constraint-preserving approximations and mesh independence. This paper presents…

We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case…

In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn--Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time…

This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov-Maxwell system. The SD scheme yields a weak formulation, that corresponds to an…

We derive a posteriori error estimates in the $L_\infty((0,T];L_\infty(\Omega))$ norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat…

Learning Gaussian Mixture Models (GMMs) is a fundamental problem in machine learning, with the Expectation-Maximization (EM) algorithm and its popular variant gradient EM being arguably the most widely used algorithms in practice. In the…

The present paper extends the theory of Adaptive Virtual Element Methods (AVEMs) to the three-dimensional meshes showing the possibility to bound the stabilization term by the residual-type error estimator. This new bound enables a…

This article introduces a novel residual-based a posteriori error estimators for the Modified Weak Galerkin (MWG) finite element method applied to the obstacle problem. To the best of the author's knowledge, this work represents the first…

We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved…

We study superconvergence property of the linear discontinuous Galerkin finite element method with the polynomial preserving recovery (PPR) and Richardson extrapolation for the two dimensional Helmholtz equation. The error estimate with…

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…

We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based…

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…