2 citations · 3 across the 13 of their papers we have counts for
7 papers · 1 filter
Optimal control of fractional diffusion with Dirac measures
Enrique Otarola, Abner J. Salgado
We study a PDE-constrained optimization problem for an elliptic equation with the spectral fractional Laplacian and a linear combination of Dirac measures as the forcing term; the…
Bochner Stability for B-stable DIRK Schemes
Anthony E. Ramirez, Abner J. Salgado
In Abner J. Salgado and Ignacio Tomas. Diagonally implicit Runge-Kutta schemes: discrete energy-balance laws and compactness properties. J. Number. Math., 31(4):313-341, 2023, the…
Self-improving properties for a class of elliptic and parabolic equations on bounded domains
Tadele Mengesha, Abner J. Salgado
We discuss self improving properties of some local and nonlocal, elliptic and parabolic, equations on bounded domains. We employ a functional analytic approach wherein the solution…
Analysis and approximation of a two-dimensional induction heating problem
Gabriel R. Barrenechea, Katherine MacKenzie, Abner Salgado
In this paper, we analyse the existence of solutions and finite element approximation of a steady-state two-dimensional induction heating problem. One of the main difficulties of t…
A pointwise tracking optimal control problem for a fractional, semilinear PDE
Enrique Otarola, Abner J. Salgado
We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fra…
Approximation of higher-order powers of the spectral fractional Laplacian via polyharmonic extension
Enrique Otárola, Abner J. Salgado
We use the polyharmonic extension approach to develop a numerical technique for discretizing higher-order powers of the spectral fractional Laplacian with .