Zobrazeno 1 - 10
of 179
pro vyhledávání: '"Bertoluzza, Silvia"'
We propose a hybridized domain decomposition formulation of the discrete fracture network model, allowing for independent discretization of the individual fractures. A natural norm stabilization, obtained by penalizing the residual measured in the no
Externí odkaz:
http://arxiv.org/abs/2407.18434
Autor:
Bertoluzza, Silvia, Burman, Erik
Introducing a coupling framework reminiscent of FETI methods, but here on abstract form, we establish conditions for stability and minimal requirements for well-posedness on the continuous level, as well as conditions on local solvers for the approxi
Externí odkaz:
http://arxiv.org/abs/2312.11733
Autor:
Bertoluzza, Silvia
We extend a localization result for the $H^{1/2}$ norm by B. Faermann to a wider class of subspaces of $H^{1/2}(\Gamma)$, and we prove an analogous result for the $H^{-1/2}(\Gamma)$ norm, $\Gamma$ being the boundary of a bounded polytopal domain $\Om
Externí odkaz:
http://arxiv.org/abs/2312.01101
We present a reduced basis method for cheaply constructing (possibly rough) approximations to the nodal basis functions of the virtual element space, and propose to use such approximations for the design of the stabilization term in the virtual eleme
Externí odkaz:
http://arxiv.org/abs/2310.00625
In this paper, we provide a theoretical analysis of the recently introduced weakly adversarial networks (WAN) method, used to approximate partial differential equations in high dimensions. We address the existence and stability of the solution, as we
Externí odkaz:
http://arxiv.org/abs/2307.05012
We propose a method, based on Artificial Neural Networks, that learns the dependence of the constant in the Poincar\'e inequality on polygonal elements of Voronoi meshes, on some geometrical metrics of the element. The cost of this kind of algorithms
Externí odkaz:
http://arxiv.org/abs/2206.10292
We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case of approxi
Externí odkaz:
http://arxiv.org/abs/2206.03449
We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local $H^1$ error in a interior subdomain is bounded by a term behaving li
Externí odkaz:
http://arxiv.org/abs/2204.09955
Publikováno v:
Computer Methods in Applied Mechanics and Engineering, Volume 400, (2022), 115454
In the framework of virtual element discretizazions, we address the problem of imposing non homogeneous Dirichlet boundary conditions in a weak form, both on polygonal/polyhedral domains and on two/three dimensional domains with curved boundaries. We
Externí odkaz:
http://arxiv.org/abs/2112.15039
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and preconditioning. Th
Externí odkaz:
http://arxiv.org/abs/2111.11085