2 citations · 3 across the 5 of their papers we have counts for
6 papers · 1 filter
Convergent, with rates, methods for normalized infinity Laplace, and related, equations
Wenbo Li, Abner J. Salgado
We propose a monotone, and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized Infinity Laplacian, which could be related to the family of…
Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties
Abner J. Salgado, Ignacio Tomas
We study diagonally implicit Runge-Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions…
Preconditioned accelerated gradient descent methods for locally Lipschitz smooth objectives with applications to the solution of nonlinear PDEs
Jea-Hyun Park, Abner J. Salgado, Steven M. Wise
We develop a theoretical foundation for the application of Nesterov's accelerated gradient descent method (AGD) to the approximation of solutions of a wide class of partial differe…
The stationary Boussinesq problem under singular forcing
Alejandro Allendes, Enrique Otarola, Abner J. Salgado
In Lipschitz two and three dimensional domains, we study the existence for the so--called Boussinesq model of thermally driven convection under singular forcing. By singular we mea…
A posteriori error estimates for the stationary Navier Stokes equations with Dirac measures
Alejandro Allendes, Enrique Otarola, Abner J. Salgado
In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier Stokes equations with singular sources on Lipsc…
Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian
Juan Pablo Borthagaray, Ricardo H. Nochetto, Abner J. Salgado
We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian. The weight is a power of the distance to the…