Related papers: The virtual element method for linear elastodynami…
In this study a stabilized finite element method for solving advection-diffusion-reaction equation with spatially variable coefficients has been carried out. Here subgrid scale approach along with algebraic approximation to the sub-scales…
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal…
We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an $H^1(\Omega)$-conforming discretization by means of VEM which can make use of general polygonal…
We initiate the design and the analysis of stabilization-free Virtual Element Methods for the laplacian problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the…
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method, for the efficient solution of very large linear systems arising from elliptic…
Finite element methods are well-known to admit robust optimal convergence on simplicial meshes satisfying the maximum angle conditions. But how to generalize this condition to polyhedra is unknown in the literature. In this work, we argue…
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…
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…
We propose and analyze an $H^2$-conforming Virtual Element Method (VEM) for the simplest linear elliptic PDEs in nondivergence form with Cordes coefficients. The VEM hinges on a hierarchical construction valid for any dimension $d \ge 2$.…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
We study the $h$- and $p$-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use…
In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential problems of the form $\Delta^p u =f$, $p\ge1$. More…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
We present a 50-line MATLAB implementation of the lowest order virtual element method for the two-dimensional Poisson problem on general polygonal meshes. The matrix formulation of the method is discussed, along with the structure of the…
In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…
We propose and analyze a linear and partitioned finite element method for fluid-shell interactions under the arbitrary Lagrangian-Eulerian (ALE) framework. We adopt the P1-bubble/P1/P1 elements for the fluid velocity, pressure, and…
We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to…
Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and…