117,311 research outputs found
Enrichment of the nonconforming virtual element method with singular functions
No full textWe construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have singularities due to the geometry of the domain. Differently from the traditional extended Galerkin method approach, based on the enrichment of local spaces with singular functions, no partition of unity is employed. Rather, the design of the method hinges upon the special structure of the nonconforming virtual element spaces. We discuss the theoretical analysis of the method and support it with several numerical experiments. We also present an orthonormalization procedure that drastically trims the ill-conditioning of the final system
A multigrid algorithm for the p -version of the virtual element method
No full textWe present a multigrid algorithm for the solution of the linear systems of equations stemming from the p-version of the virtual element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed decreasing progressively the polynomial approximation degree of the virtual element space, as in standard p-multigrid schemes. The construction of the interspace operators relies on auxiliary virtual element spaces, where it is possible to compute higher order polynomial projectors. We prove that the multigrid scheme is uniformly convergent, provided the number of smoothing steps is chosen sufficiently large. We also demonstrate that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom that can be employed to accelerate the convergence of classical Krylov-based iterative schemes. Numerical experiments validate the theoretical results
Basic principles of hp virtual elements on quasiuniform meshes
No full textIn the present paper we initiate the study of hp Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size h and in the polynomial degree p in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included
Stability Analysis of Polytopic Discontinuous Galerkin Approximations of the Stokes Problem with Applications to Fluid–Structure Interaction Problems
No full textWe present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial approximation order of the velocity and pressure approximation spaces. To this aim, we employ a generalized inf-sup condition with a pressure stabilization term. We also prove a priori hp-version error estimates in suitable norms. We numerically check the behaviour of the inf-sup constant and the order of convergence with respect to the mesh configuration, the mesh-size, and the polynomial degree. Finally, as a relevant application of our analysis, we consider the PolyDG approximation for a 2D fluid–structure interaction problem and we numerically explore the stability properties of the method
The p- and hp-versions of the virtual element method for elliptic eigenvalue problems
No full textWe discuss the p- and hp-versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schrödinger equation with a pseudo-potential term. As an interesting byproduct, we present for the first time in literature an explicit construction of the stabilization of the mass matrix. We present in detail the analysis of the p-version of the method, proving exponential convergence in the case of analytic eigenfunctions. The theoretical results are supplied with a wide set of experiments. We also show numerically that, in the case of eigenfunctions with finite Sobolev regularity, an exponential approximation of the eigenvalues in terms of the cubic root of the number of degrees of freedom can be obtained by employing hp-refinements. Importantly, the geometric flexibility of polygonal meshes is exploited in the construction of the hp-spaces
The - and -versions of the virtual element method for elliptic eigenvalue problems
No full textWe discuss the p- and hp-versions of the virtual element method for the approximation
of eigenpairs of elliptic operators with a potential term on polygonal meshes. An
application of this model is provided by the Schrödinger equation with a pseudo-
potential term. As an interesting by product, we present for the first time in literature
an explicit construction of the stabilization of the mass matrix. We present in detail
the analysis of the p-version of the method, proving exponential convergence in the
case of analytic eigenfunctions. The theoretical results are supplied with a wide set
of experiments. We also show numerically that, in the case of eigenfunctions with
finite Sobolev regularity, an exponential approximation of the eigenvalues in terms of
the cubic root of the number of degrees of freedom can be obtained by employing
hp-refinements. Importantly, the geometric flexibility of polygonal meshes is exploited
in the construction of the hp-spaces
Understanding Oxygen Release from Nanoporous Perovskite Oxides and Its Effect on the Catalytic Oxidation of CH4and CO
No full textThe design of nanoporous perovskite oxides is considered an efficient strategy to develop performing, sustainable catalysts for the conversion of methane. The dependency of nanoporosity on the oxygen defect chemistry and the catalytic activity of perovskite oxides toward CH4 and CO oxidation was studied here. A novel colloidal synthesis route for nanoporous, high-temperature stable SrTi0.65Fe0.35O3-δ with specific surface areas (SSA) ranging from 45 to 80 m2/g and pore sizes from 10 to 100 nm was developed. High-temperature investigations by in situ synchrotron X-ray diffraction (XRD) and TG-MS combined with H2-TPR and Mössbauer spectroscopy showed that the porosity improved the release of surface oxygen and the oxygen diffusion, whereas the release of lattice oxygen depended more on the state of the iron species and strain effects in the materials. Regarding catalysis, light-off tests showed that low-temperature CO oxidation significantly benefitted from the enhancement of the SSA, whereas high-temperature CH4 oxidation is influenced more by the dioxygen release. During isothermal long-term catalysis tests, however, the continuous oxygen release from large SSA materials promoted both CO and CH4 conversion. Hence, if SSA maximization turned out to efficiently improve low-temperature and long-term catalysis applications, the role of both reducible metal center concentration and crystal structure cannot be completely ignored, as they also contribute to the perovskite oxygen release properties
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