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Topografia Eeg Computerizzata Durante Test Cognitivi In Età Evolutiva. Considerazioni Metodologiche.
No full textAn hp-Hybrid High-Order method for variable diffusion on general meshes
No full textIn this work, we introduce and analyze a hp-Hybrid High-Order method for a variable diffusion problem. The proposed method is valid in arbitrary space dimension and for fairly general polytopal meshes. Variable approximation degrees are also supported. We formulate hp-convergence estimates for both the energy- and L2-norms of the error, which are the first results of this kind for Hybrid High-Order methods. The estimates are fully robust with respect to the heterogeneity of the diffusion coefficient, and show only a mild dependence on its (local) anisotropy. The ex- pected exponential convergence behaviour is numerically shown on a variety of meshes for both isotropic and strongly anisotropic diffusion problems
Mass Preserving Finite Element Implementations of Level Set Method
No full textIn the last two decades, the level set method has been extensively used for the numerical solution of interface problems in different domains. The basic idea is to embed the interface as the level set of a regular function. In this paper we focus on the numerical solution of interface advection equations appearing in free-surface fluid dynamics problems, where naive finite element implementations are unsatisfactory. As a matter of fact, practitioners in fluid dynamics often complain that the mass of each fluid component is not conserved, a phenomenon which is therefore often referred to as mass loss. In this paper we propose and compare two finite element implementations that cure this ill-behaviour without the need to resort to combined strategies (such as e.g. particle level set). The first relies on a discontinuous Galerkin discretization, which is known to give very good performance when facing hyperbolic problems; the second is a stabilized continuous FEM implementation based on the stabilization method presented in [16], which is free from many of the problems that classical methods exhibit when applied to unsteady problems
A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity
Full text linkIn this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients
High-order discontinuous Galerkin solution of low- and high-Reynolds number compressible flows
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Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
No full textDiscontinuous Skeletal methods approximate the solution of boundary-value problems by attaching discrete unknowns to mesh faces (hence the term skeletal) while allowing these discrete unknowns to be chosen independently on each mesh face (hence the term discontinuous). Cell-based unknowns, which can be eliminated locally by a Schur complement technique (also known as static condensation), are also used in the formulation. Salient examples of high-order Discontinuous Skeletal methods are Hybridizable Discontinuous Galerkin methods and the recently-devised Hybrid High-Order methods. Some major benefits of Discontinuous Skeletal methods are that their construction is dimension-independent and that they offer the possibility to use general meshes with polytopal cells and non-matching interfaces. In this work, we show how this mathematical flexibility can be efficiently replicated in a numerical software using generic programming. We describe a number of generic algorithms and data structures for high-order Discontinuous Skeletal methods within a “write once, run on any kind of mesh” framework. The computational efficiency of the implementation is assessed on the Poisson model problem discretized using various polytopal meshes and the Hybrid High-Order method
Analisi Topografica Computerizzata Dei Potenziali Evocati Visivi In Soggetti In Età Evolutiva.
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