From the 1 of 9 linked papers with an AI index.
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Asymptotic compatibility of parametrized optimal design problems
Tadele Mengesha, Abner J. Salgado, Joshua M. Siktar
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent,…
A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian
Abner J. Salgado, Shane E. Sawyer
We present a technique for approximating solutions to the spectral fractional Laplacian, which is based on the Caffarelli-Silvestre extension and diagonalization. Our scheme uses t…
Monotone two-scale methods for a class of integrodifferential operators and applications
Juan Pablo Borthagaray, Ricardo H. Nochetto, Abner J. Salgado +1
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order , . We apply it to develop numerical schemes, and derive poin…
Analysis and finite element approximation of a diffuse interface approach to the Stokes--Biot coupling
Francis R. A. Aznaran, Martina BukaÄ, Boris Muha +1
We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressibl…
Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes
Tadele Mengesha, Enrique Otarola, Abner J. Salgado
We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is as…