相关论文: SUPG-stabilized Virtual Elements for diffusion-con…

We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of 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…

Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide…

This paper contains construction and analysis a finite element approximation for convection dominated diffusion problems with full coefficient matrix on general simplicial partitions in $R^d$, $d=2,3$. This construction is quite close to…

We present stability and error analysis for algebraic flux correction schemes based on monolithic convex limiting. For a continuous finite element discretization of the time-dependent advection equation, we prove global-in-time existence…

We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…

We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…

We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…

A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…

This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…

In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…

We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…

We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds from the cases where convection or reaction is not present to convection-or…

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate…

In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…

We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations.…

For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…

We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear form from the elemental nonconforming virtual element…

We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, with decomposition…

Let us consider the singularly perturbed model problem $Lu:=-\varepsilon\Delta u-bu_x+c u =f$ with homogeneous Dirichlet boundary conditions on $\Gamma=\partial\Omega$ $u|_\Gamma =0$ on the unit-square $\Omega=(0,1)^2$. Assuming that $b>0$…