145 citations · 506 across the 57 of their papers we have counts for
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Finite element approximation of the Isaacs equation
Abner J. Salgado, Wujun Zhang
We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size whereas the coarse scale is dictated by…
The equations of ferrohydrodynamics: modeling and numerical methods
Ricardo H. Nochetto, Abner J. Salgado, Ignacio Tomas
We discuss the equations describing the motion of ferrofluids subject to an external magnetic field. We concentrate on the model proposed by R. Rosensweig, provide an appropriate d…
A PDE Approach to Numerical Fractional Diffusion
Ricardo H. Nochetto, Enrique Otarola, Abner J. Salgado
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approxima…
Finite element approximation of the parabolic fractional obstacle problem
Enrique Otarola, Abner J. Salgado
We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a non…
Some applications of weighted norm inequalities to the error analysis of PDE constrained optimization problems
Harbir Antil, Enrique Otarola, Abner J. Salgado
The purpose of this work is to illustrate how the theory of Muckenhoupt weights, Muckenhoupt weighted Sobolev spaces and the corresponding weighted norm inequalities can be used in…
A fractional space-time optimal control problem: analysis and discretization\
Harbir Antil, Enrique Otarola, Abner J. Salgado
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders and $γ\in…