145 citations · 609 across the 61 of their papers we have counts for
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Discrete ABP Estimate and Convergence Rates for Linear Elliptic Equations in Non-divergence Form
Ricardo H. Nochetto, Wujun Zhang
We design a two-scale finite element method (FEM) for linear elliptic PDEs in non-divergence form in a bounded but not necessarily convex domain and st…
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 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…
Optimal Control of a Free Boundary Problem with Surface Tension Effects: A Priori Error Analysis
Harbir Antil, Ricardo H. Nochetto, Patrick Sodré
We present a finite element method along with its analysis for the optimal control of a model free boundary problem with surface tension effects, formulated and studied in \cite{HA…
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…