相关论文: A $C^0$-continuous nonconforming virtual element m…
We present a Virtual Element Method for the 3D linear elasticity problems, based on Hellinger-Reissner variational principle. In the framework of the small strain theory, we propose a low-order scheme with a-priori symmetric stresses and…
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…
This study presents the application of variable-order (VO) fractional calculus to the modeling of nonlocal solids. The reformulation of nonlocal fractional-order continuum mechanic framework, by means of VO kinematics, enables a unique…
This paper analyses conforming and nonconforming virtual element formulations of arbitrary polynomial degrees on general polygonal meshes for the coupling of solid and fluid phases in deformable porous plates. The governing equations…
In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual element method (VEM) for solving the coupled Poisson-Nernst-Planck (PNP) and Navier--Stokes (NS) equations modeling microfluidic and…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries,…
We present the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov-Galerkin (VEM-SUPG) stabilization for the numerical resolution of…
In this paper, we propose a conservative nonconforming virtual element method for the full stationary incompressible magnetohydrodynamics model. We leverage the virtual element satisfactory divergence-free property to ensure mass…
We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration…
We develop a formal construction of a pointwise divergence-free basis in the nonconforming virtual element method of arbitrary order for the Stokes problem introduced in [19]. The proposed construction can be seen as a generalization of the…
The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within…
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…
The $H^m$-nonconforming virtual elements of any order $k$ on any shape of polytope in $\mathbb R^n$ with constraints $m>n$ and $k\geq m$ are constructed in a universal way. A generalized Green's identity for $H^m$ inner product with $m>n$…
We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
In this paper, we propose a novel bounded asymmetric elastic net ($L_{baen}$) loss function and combine it with the support vector machine (SVM), resulting in the BAEN-SVM. The $L_{baen}$ is bounded and asymmetric and can degrade to the…
The Virtual Element Method for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the presence…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…