Related papers: A Virtual Element Method for the wave equation on …
We consider the efficient numerical approximation of acoustic wave propagation in time domain by a finite element method with mass lumping. In the presence of internal damping, the problem can be reduced to a second order formulation in…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…
The mesh flexibility offered by the virtual element method through the permission of arbitrary element geometries, and the seamless incorporation of `hanging' nodes, has made the method increasingly attractive in the context of adaptive…
In this paper, we are concerned with the numerical treatment of boundary integral equations by means of the adaptive wavelet boundary element method (BEM). In particular, we consider the second kind Fredholm integral equation for the double…
Virtual element methods is a new promising finite element methods using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In this paper, we take a different viewpoint. We try to uncover…
We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component…
In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is…
In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM)…
In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose $C^1$ conforming virtual element method (VEM) of arbitrary order,…
In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…
A two-grid scheme based on mixed finite-element approximations to the incompressible Navier-Stokes equations is introduced and analyzed. In the first level the standard mixed finite-element approximation over a coarse mesh is computed. In…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its…