Related papers: Interpolation and stability estimates for edge and…
We present numerical tests of the Virtual Element Method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order "polynomial" degree (up to $p=10$). Besides, we discuss possible reasons for which the…
This paper considers the problem of nonlinear attitude estimation for a rigid body system using intermittent and multi-rate inertial vector measurements as well as continuous (high-rate) angular velocity measurements. Two types of hybrid…
In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric…
We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual element…
We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the…
We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal ($H^1$-conforming) elements, to a more general framework. Then we apply the general strategy to the case of $H(div)$ and…
In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
In this paper, we study arbitrary order extended finite element (XFE) methods based on two discontinuous Galerkin (DG) schemes in order to solve elliptic interface problems in two and three dimensions. Optimal error estimates in the…
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…
In this work we consider the two dimensional instationary Navier-Stokes equations with homogeneous Dirichlet/no-slip boundary conditions. We show error estimates for the fully discrete problem, where a discontinuous Galerkin method in time…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or approximation of vector-valued functions on Delaunay meshes in…
We rewrite the standard nodal virtual element method as a generalised gradient method. This re-formulation allows for computing a reliable and efficient error estimator by locally reconstructing broken fluxes and potentials on elemental…
In this paper we analyze a virtual element method for the two dimensional elasticity spectral problem allowing small edges. Under this approach, and with the aid of the theory of compact operators, we prove convergence of the proposed VEM…
We investigate fundamental localized modes in 2D lattices with an edge (surface). Interaction with the edge expands the stability area for ordinary solitons, and induces a difference between perpendicular and parallel dipoles; on the…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency…
We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) for the Poisson problem. The method allows the definition of bilinear forms that do not require a stabilization term, thanks to the exploitation…