242 citations · 463 across the 11 of their papers we have counts for
13 papers
Neural Very Weak Formulations enabling Hardware-Oriented deep PDE solvers
Gabriel Acosta, Francisco Bersetche
We show, as a proof of concept, that least-squares very weak formulations of elliptic problems can be effectively discretized by neural networks possessing low regularity, provided…
The Fractional Korn Inequality on Uniform Domains and New Korn Inequalities for Truncated Seminorms
Gabriel Acosta, Irene Drelichman, Ricardo Durán +2
We prove the so-called second case of the fractional Korn inequality for uniform domains. We obtain this result as an application of a novel fractional Korn-type inequality formula…
A deep first-order system least squares method for the obstacle problem
Gabriel Acosta, Eugenia Belén, Francisco M. Bersetche +1
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex min…
A domain decomposition scheme for couplings between local and nonlocal equations
Gabriel Acosta, Francisco M. Bersetche, Julio D. Rossi
We study a natural alternating method of Schwarz type (domain decomposition) for certain class of couplings between local and nonlocal operators. We show that our method fits into…
Weighted fractional Sobolev spaces as interpolation spaces in bounded domains
Gabriel Acosta, Irene Drelichman, Ricardo G. Durán
We characterize the real interpolation space between a weighted space and a weighted Sobolev space in arbitrary bounded domains in , with weights that are posit…
Coupling local and nonlocal equations with Neumann boundary conditions
Gabriel Acosta, Francisco Bersetche, Julio Rossi
We introduce two different ways of coupling local and nonlocal equations with Neumann boundary conditions in such a way that the resulting model is naturally associated with an ene…
Local and nonlocal energy-based coupling models
Gabriel Acosta, Francisco M. Bersetche, Julio D. Rossi
In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the firs…
Numerical approximations for a fully fractional Allen-Cahn equation
Gabriel Acosta, Francisco Bersetche
A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractiona…
Finite element approximations of the nonhomogeneous fractional Dirichlet problem
Gabriel Acosta, Juan Pablo Borthagaray, Norbert Heuer
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and…
Finite element approximations for fractional evolution problems
Gabriel Acosta, Francisco M. Bersetche, Juan Pablo Borthagaray
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided…
A short FE implementation for a 2d homogeneous Dirichlet problem of a Fractional Laplacian
Gabriel Acosta, Francisco M. Bersetche, Juan Pablo Borthagaray
In \cite{AcostaBorthagaray}, a complete -dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we pro…
Regularity theory and high order numerical methods for the (1d)-Fractional Laplacian
Gabriel Acosta, Juan Pablo Borthagaray, Oscar Bruno +1
This paper presents regularity results and associated high-order numerical methods for one-dimensional Fractional-Laplacian boundary-value problems. On the basis of a factorization…
A fractional Laplace equation: regularity of solutions and Finite Element approximations
Gabriel Acosta, Juan Pablo Borthagaray
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are…