- Assistant Professor.
- PhD in Mathematics, Universidad de Buenos Aires (2017).
- Research area: Numerical Analysis.
- Contact: jpborthagaray@unorte.edu.uy
Previously I have worked in the Department of Mathematics at University of Maryland (postdoc, 2017–2019); in the Ciclo Básico Común at Universidad de Buenos Aires (2013–2017); in the Facultad de Ingeniería (2011–2012); and in the Facultad de Ciencias (2009–2011) at Universidad de la República.
Research
My research area lies between the numerical analysis and the analysis of partial differential equations (PDEs). This includes mainly finite element methods, the analysis and design of numerical methods for nonlocal operators and the study of certain geometric PDEs.
Published articles:
F.M. Bersetche, J.P. Borthagaray. Finite element approximation of fractional Neumann problems. IMA Journal of Numerical Analysis, drab064.
J.P. Borthagaray, W. Li, R.H. Nochetto. Finite element algorithms for nonlocal minimal graphs. Mathematics in Engineering, 4(2):1-29, 2022.
J.P. Borthagaray, D. Leykekhman, R.H. Nochetto. Local energy estimates for the fractional Laplacian. SIAM Journal on Numerical Analysis, 59(4):1918–1947, 2021.
J.P. Borthagaray, S.W. Walker. The Q-tensor Model with Uniaxial Constraint. Handbook of Numerical Analysis, 22:313–382, 2021.
J.P. Borthagaray, W. Li, R.H. Nochetto. Linear and nonlinear fractional elliptic problems. In 75 Years of Mathematics of Computation, Contemporary Mathematics, 754:69-92. American Mathematical Society, Providence, 2020.
J.P. Borthagaray, R.H. Nochetto, S.W. Walker. A structure-preserving FEM for the uniaxially constrained Q-tensor model of nematic liquid crystals. Numerische Mathematik, 145(4):837-881, 2020.
J.P. Borthagaray, R.H. Nochetto, A.J Salgado. Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. Mathematical Models and Methods in Applied Sciences, 29(14):2679–2717, 2019.
J.P. Borthagaray, W. Li, R.H. Nochetto. Finite element discretizations of nonlocal minimal graphs: Convergence. Nonlinear Analysis, 189:111566, 2019.
J.P Borthagaray, P. Ciarlet Jr. On the convergence in $H^1$-norm for the fractional Laplacian. SIAM Journal on Numerical Analysis, 57(4):1723–1743, 2019.
G. Acosta, F.M. Bersetche, J.P. Borthagaray. Finite element approximations for fractional evolution problems. Fractional Calculus and Applied Analysis, 22(3):767–794, 2019.
G. Acosta, J.P. Borthagaray, N. Heuer. Finite element approximations of the nonhomogeneous fractional Dirichlet problem. IMA Journal on Numerical Analysis, 39(3):1471–1501, 2019.
J.P. Borthagaray, L.M. Del Pezzo, S. Martínez. Finite element approximation for the fractional eigenvalue problem. Journal of Scientific Computing, 77(1):308–329, 2018.
A. Bonito, J.P. Borthagaray, R.H. Nochetto, E. Otárola, A.J. Salgado. Numerical methods for fractional diffusion. Computing and Visualization in Science, 19(5–6):19–46, 2018.
G. Acosta, J.P. Borthagaray, O. Bruno, M. Maas. Regularity theory and high order numerical methods for the (1d)-Fractional Laplacian. Mathematics of Computation, 87(312):1821–1857, 2018.
G. Acosta, F.M. Bersetche, J.P. Borthagaray. A short FE implementation for a 2D homogeneous Dirichlet problem of a fractional Laplacian. Computers and Mathematics with Applications, 74(4):784–816, 2017.
G. Acosta, J.P. Borthagaray. A fractional Laplace equation: regularity of solutions and finite element approximations. SIAM Journal on Numerical Analysis, 55(2):472–495, 2017.
J.P. Borthagaray, J. Fernández Bonder, A. Silva. A mass transportation approach for Sobolev inequalities in variable exponent spaces. Manuscripta Mathematica, 151(1):133–146, 2016.
Preprints:
J.P. Borthagaray, R.H. Nochetto. Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains.
J.P. Borthagaray, R.H. Nochetto. Constructive approximation on graded meshes for the integral fractional Laplacian.
J.P. Borthagaray, R.H. Nochetto, S. Wu, J. Xu. Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains.