145 citations · 353 across the 46 of their papers we have counts for
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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…
A piecewise linear FEM for an optimal control problem of fractional operators: error analysis on curved domains
Enrique Otarola
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second od…
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…