139 citations · 140 across the 8 of their papers we have counts for
11 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…
A nonlocal coupled system: analysis and discretization
Francisco Bersetche, Enrique Otarola, Daniel Quero
We analyze a nonlocal coupled system arising as the Euler--Lagrange equations of an energy functional involving regional fractional Laplacians of orders and ($ 0 < s_1,…
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…
A deep first-order system least squares method for solving elliptic PDEs
Francisco M. Bersetche, Juan Pablo Borthagaray
We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing…
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…
Finite element approximation of fractional Neumann problems
Francisco M. Bersetche, Juan Pablo Borthagaray
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation…
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 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…