My research interests are mainly in Partial Differential Equations (PDE) and Numerical Analysis of PDE. These include theoretical aspects of approximation theory, regularity theory and continuum mechanics. Please take a look at my Google Scholar, ORCID, ResearchGate and MathSciNet profiles for my pre-prints and publications (you can also see them listed below).
I have collaborated with the following researchers and students:
Leonardo E. Figueroa, professor at Universidad de Concepción (UDEC), Chile. Website
Gabriel N. Gatica, professor at Universidad de Concepción (UDEC), Chile. Website
Ricardo Ruiz-Baier, professor at Monash University, Australia. Website
Sergio Caucao, professor at Universidad Católica de la Santísima Concepción (UCSC). Website
Mario Álvarez, professor at Universidad de Costa Rica.
Sebastián Domínguez-Rivera, researcher at Siemens Canada. Website
Esteban Henríquez, PhD student at University of Waterloo, Canada. Website
Alejandro A. Hopper, undergraduate student at Universidad de Concepción (UDEC), Chile.
In preparation
G.A. Benavides, R.H. Nochetto and M. Shakipov. Well-posedness of the hydrodynamic Surface Beris–Edwards model for Nematic Liquid Crystals
G.A. Benavides, R.H. Nochetto and M. Shakipov. Lᵖ-based Sobolev theory for PDEs on closed manifolds of minimal regularity: Part II: Vector-valued problems
G.A. Benavides, R.H. Nochetto and M. Shakipov. Lᵖ-based Sobolev theory for PDEs on closed manifolds of minimal regularity: Part I: Scalar elliptic equations
Published
M. Álvarez, G.A. Benavides, G.N. Gatica, E. Henríquez and R. Ruiz-Baier. Banach spaces-based mixed finite element methods for a steady sedimentation-consolidation system. Calcolo (in press) Preprint
G.A. Benavides, S. Domínguez-Rivera. Korn’s inequality in anisotropic Sobolev spaces. Journal of Applied Analysis, vol. 29, no. 2, 2023, pp. 367-377. (2023). Article Preprint
G.A. Benavides, S. Caucao, G.N. Gatica and A.A. Hopper. A new non-augmented and momentum-conserving fully-mixed finite element method for a coupled flow-transport problem. Calcolo 59 (2022), no. 1, Paper No. 6, 44 pp. Article Preprint
G.A. Benavides and L.E. Figueroa. Orthogonal polynomial projection error in Dunkl–Sobolev norms in the ball. Journal of Approximation Theory, vol. 261, 105495 (2021). Article Preprint
G.A. Benavides, S. Caucao, G.N. Gatica and A.A. Hopper. A Banach spaces--based analysis of a new mixed-primal finite element method for a coupled flow--transport problem. Computer Methods in Applied Mechanics and Engineering, vol. 371, Art. Num. 113285, (2020). Article Preprint
Orthogonal polynomials with reflection-invariant weights. Ingeniería Civil Matemática thesis, Universidad de Concepción (2020). Thesis Video (in Spanish)