Related papers: A High-order Arbitrary Lagrangian-Eulerian Virtual…
We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving moving boundaries. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary…
We develop a numerical assessment of the Virtual Element Method for the discretization of a diffusion-reaction model problem, for higher "polynomial" order k and three space dimensions. Although the main focus of the present study is to…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method and a second-order projection method along the trajectories of the…
We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [59] the problem is supposed to have a unique solution, but…
We present a one-dimensional high-order moving-mesh finite element method for moving boundary problems where the boundary velocity depends implicitly on the solution in the interior of the domain. The method employs a conservative arbitrary…
We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to…
This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…
We propose an efficient method for the numerical approximation of a general class of two dimensional semilinear parabolic problems on polygonal meshes. The proposed approach takes advantage of the properties of the serendipity version of…
In this work, we have discretized a system of time-dependent nonlinear convection-diffusion-reaction equations with the virtual element method over the spatial domain and the Euler method for the temporal interval. For the nonlinear…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
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…
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which employs a semi-Lagrangian approach to approximate in time both the advective and the diffusive…
In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and…
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…
A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is prescribed by a discretized dynamical system for the nodal…
In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved…