9 papers
A priori error analysis for the Shliomis ferrofluid model without magnetic regularization
Gonzalo A. Benavides, Ricardo H. Nochetto
We develop and analyze a family of conforming, energy-stable spatial semidiscretizations of the Shliomis ferrofluid model in two and three space dimensions. Unlike many existing nu…
Convergence of a fully discrete finite element method for the Beris-Edwards system of liquid crystal dynamics
Gonzalo A. Benavides, Franziska Weber
We propose and analyze a fully discrete finite element scheme for the Beris-Edwards system of nematic liquid crystal dynamics, in which the incompressible Navier-Stokes equations a…
Existence of weak solutions of the surface Beris-Edwards model
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
We prove the existence of weak solutions to the surface Beris-Edwards model for nematic liquid crystals posed on a -dimensional () closed hypersurface of class $C…
Ferrofluids: Modeling and Approximation
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
Starting from Maxwell's and linear momentum balance equations, we derive a ferrofluid model using the generalized Onsager's principle. Guided by a discrete perturbation estimate, w…
-based Sobolev theory on closed manifolds of minimal regularity: Scalar Elliptic Equations
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
This paper and its follow-up arXiv:2508.11109 are concerned with the well-posedness and -based Sobolev regularity for appropriate weak formulations of a family of pro…
-based Sobolev theory on closed manifolds of minimal regularity: Vector-valued problems
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
This paper is the second part of a two-paper series, initiated in arXiv:2603.02163 for scalar PDEs on hypersurfaces, and is concerned with the well-posedness and -bas…
Korn's inequality in anisotropic Sobolev spaces
Gonzalo A. Benavides, Sebastián A. Domínguez-Rivera
Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to t…
The evolution of the COVID-19 pandemic in Chile during 2020: a data perspective
Gonzalo A. Benavides, Francisca Larach, Vicente Marchant +4
The COVID-19 pandemic has had a great impact in most countries worldwide, in particular impacting Chile greatly to become one of the worst hit countries in the world, despite its l…
Orthogonal polynomial projection error in Dunkl-Sobolev norms in the ball
Gonzalo A. Benavides, Leonardo E. Figueroa
We study approximation properties of weighted -orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of t…