Related papers: A stabilized virtual element framework for the ste…
We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…
In this paper, we introduce a new Virtual Element Method (VEM) not requiring any stabilization term based on the usual enhanced first-order VEM space. The new method relies on a modified formulation of the discrete diffusion operator that…
We propose and analyze an augmented mixed finite element method for the pseudostress-velocity formulation of the stationary convective Brinkman-Forchheimer problem in $\mathrm{R}^d$, $d\in \{2,3\}$. Since the convective and Forchheimer…
In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime (r > 2) including both…
We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…
We study the weak Galerkin finite element method for Stokes problem. A new weak Galerkin finite element velocity-pressure space pair is presented which satisfies the discrete inf-sup condition. Based on this space pair, we establish a…
We study a stationary model of doubly diffusive flows with temperature-dependent viscosity on bounded Lipschitz domains in two and three dimensions. A new well-posedness and regularity analysis of weak solutions under minimal assumptions on…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with…
The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and…
In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
In this paper, we consider a semi-linear stochastic strongly damped wave equation driven by additive Gaussian noise. Following a semigroup framework, we establish existence, uniqueness and space-time regularity of a mild solution to such…
In this paper we consider a class of fictitious domain finite element methods known from the literature. These methods use standard finite element spaces on a fixed unfitted triangulation combined with the Nitsche technique and a ghost…
We discuss the approximation of eigenvalue problems associated with elliptic partial differential equations using the virtual element method. After recalling the abstract theory, we present a model problem, describing in detail the features…
This paper proposes a novel first-order and a novel second-order fully discrete virtual element schemes based on the scalar auxiliary variable method for the three dimensional inductionless magnetohydrodynamics problem. The backward Eular…