Related papers: SUPG-stabilized Virtual Elements for diffusion-con…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation…
We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm can be utilized to improve…
This paper presents a mass-lumped Virtual Element Method (VEM) with explicit Strong Stability-Preserving Runge--Kutta (SSP-RK) time integration for two-dimensional parabolic problems on general polygonal meshes. A diagonal mass matrix is…
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…
The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…
We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep…
In this paper, we first devise an ensemble hybridizable discontinuous Galerkin (HDG) method to efficiently simulate a group of parameterized convection diffusion PDEs. These PDEs have different coefficients, initial conditions, source terms…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
In this paper, we establish an a priori error analysis of HDG methods with two types of stabilization parameter applied to convection dominated diffusion problem. We show that, using polynomials of degree no greater than k, L2 error of the…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial…
For singularly perturbed convection-diffusion problems, supercloseness analysis of finite element method is still open on Bakhvalov-type meshes, especially in the case of 2D. The difficulties arise from the width of the mesh in the layer…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
In this paper we analyze a lowest order virtual element method for the load classic reaction-convection-diffusion problem and the convection-diffusion spectral problem, where the assumptions on the polygonal meshes allow to consider small…
Numerical methods for hyperbolic PDEs require stabilization. For linear acoustics, divergence-free vector fields should remain stationary, but classical Finite Difference methods add incompatible diffusion that dramatically restricts the…
In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Darcy type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation…
In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection- diffusion type is considered on the interval [0, 1]. The components of the solution of this…