145 citations · 353 across the 46 of their papers we have counts for
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Convergence rates for the classical, thin and fractional elliptic obstacle problems
Ricardo H. Nochetto, Enrique Otárola, Abner J. Salgado
We review the finite element approximation of the classical obstacle problem in energy and max-norms and derive error estimates for both the solution and the free boundary. On the…
A FEM for an optimal control problem of fractional powers of elliptic operators
Harbir Antil, Enrique Otarola
We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dir…
A PDE approach to fractional diffusion: a posteriori error analysis
Long Chen, Ricardo H. Nochetto, Enrique Otárola +1
We derive a computable a posteriori error estimator for the -harmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet…
A PDE approach to space-time fractional parabolic problems
Ricardo H. Nochetto, Enrique Otarola, Abner J. Salgado
We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert…
Multilevel methods for nonuniformly elliptic operators
Long Chen, Ricardo H. Nochetto, Enrique Otarola +1
We develop and analyze multilevel methods for nonuniformly elliptic operators whose ellipticity holds in a weighted Sobolev space with an --Muckenhoupt weight. Using the so-ca…
Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications
Ricardo H. Nochetto, Enrique Otarola, Abner J. Salgado
We develop a constructive piecewise polynomial approximation theory in weighted Sobolev spaces with Muckenhoupt weights for any polynomial degree. The main ingredients to derive op…