Abner J. Salgado
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Publications
In mathematics, refereed journal articles are considered the main vehicle of dissemination of original research. Because of the nature of mathematical research authors are considered on equal footing and are always listed in alphabetical order. In other words, as opposed to other disciplines, there is no "first author". Articles indicated as "accepted" have been accepted for publication by the journal's editorial board, and are awaiting publication following the journal backlog.
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Preprints

W. Li and A.J. Salgado.
Time fractional gradient flows: Theory and numerics.
arXiv

J.H. Park, A.J. Salgado, and S.M. Wise.
Preconditioned accelerated gradient descent methods for locally Lipschitz smooth objectives with applications to the solution of nonlinear PDEs.
arXiv

E. Otárola, and A.J. Salgado.
On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra.
arXiv
Published or Accepted for Publication

Z. Kinfe Birhanu, T. Mengesha, and A.J. Salgado.
The Darcy problem with porosity depending exponentially on the pressure.
Journal of Computational and Applied Mathematics (accepted), 2021.

J. Guzmán, and A.J. Salgado.
Estimation of the continuity constants for Bogovskii and regularized Poincaré integral operators. Journal of Mathematical Analysis and Applications, Volume 502 Issue 1, 125246.

A. Allendes, E. Otárola, and A.J. Salgado.
The stationary Boussinesq problem under singular forcing.
M3AS Volume No. 31, Issue No. 04, pp. 2021  827, 2021.

A. Allendes, E. Otárola, and A.J. Salgado.
A posteriori error estimates for the stationary Navier Stokes equations with Dirac measures. SIAM J. Sci. Comput., 42(3), A1860A1884.

R.G. Durán, E. Otárola, A.J. Salgado.
Stability of the Stokes projection on weighted spaces and applications. Math. Comp. 89 (2020), 15811603.
DOI: 10.1090/mcom/3509

J.P. Borthagaray, R.H. Nochetto, and A.J. Salgado.
Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. M3AS Vol. 29, No. 14, pp. 26792717 (2019).

M. Neilan, A.J. Salgado and W. Zhang.
The MongeAmpere equation.
Handbook of Numerical Analysis, Vol. 21: Geometric Partial Differential Equations  Part I. 2020.

A. Bonito, W. Lei, and A.J. Salgado.
Finite element approximation of an obstacle problem for a class of integrodifferential operators.
ESAIM: M2AN, 54 1 (2020) 229253 .

E. Otárola, A.J. Salgado.
A weighted setting for the stationary Navier Stokes equations under singular forcing.
Appl. Math. Lett. 99 (2020), 105933.

E. Otárola, R. Rankin and A.J. Salgado.
Maximumnorm a posteriori error estimates for an optimal control problem.
Computational Optimization and Applications. July 2019, Volume 73, Issue 3, pp 9971017

F. Fuica, E. Otárola, and A.J. Salgado.
An a posteriori error analysis of an elliptic optimal control problem in measure space.
Comput. Math. Appl. 77 (2019), no. 10, 26592675.

A. Allendes, E. Otárola, and A.J. Salgado.
A posteriori error estimates for the Stokes problem with singular sources.
Comput. Methods Appl. Mech. Engrg. 345 (2019), 10071032.

E. Otárola and A.J. Salgado.
The Poisson and Stokes problems on weighted spaces in Lipschitz domains and under singular forcing.
Journal of Mathematical Analysis and Applications, Volume 471, Issues 12, March 2019, Pages 599612.

A.J. Salgado and W. Zhang.
Finite element approximation of the Isaacs equation.
ESAIM: M2AN 53 (2019) 351374.

E. Otárola and A.J. Salgado.
Regularity of solutions to spacetime fractional wave equations: a PDE approach.
FCAA Volume 21, Issue 5 (2018), p. 1262.

L. Banjai, J.M. Melenk, R.H. Nochetto, E. Otárola, A.J. Salgado and Ch. Schwab.
Tensor FEM for spectral fractional diffusion.
Found. Comput. Math. 19 (2019), no. 4, 901962.

H. Antil, E. Otárola and A.J. Salgado.
Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects.
Journal of Scientific Computing, Volume 77, Issue 1, pp 204224.
DOI: 10.1007/s1091501807030

M.A. Olshanskii, L.G. Rebholz and A.J. Salgado.
On wellposedness of a velocityvorticity formulation of the NavierStokes equations with noslip boundary conditions.
DCDS, 38(7): 34593477, 2018.

A. Allendes, E. Otárola, R. Rankin and A.J. Salgado.
An a posteriori error analysis for an optimal control problem with point sources.
ESAIM, M2AN Math. Model. Numer. Anal., Volume 52 (2018), number 5, 16171650.
DOI: 10.1051/m2an/2018010

A. Bonito, J.P. Borthagaray, R.H. Nochetto, E. Otárola and A.J. Salgado.
Numerical methods for fractional diffusion.
Comput. Vis. Sci. 19 (2018), no. 56, 1946.

E. Otárola and A.J. Salgado.
Sparse optimal control for fractional diffusion.
Comput. Methods Appl. Math. 18 (2018), no. 1, 95–110.

M. Neilan, A.J. Salgado and W. Zhang.
Numerical analysis of strongly nonlinear PDEs.
Acta Numerica, Volume 26 2017, pp. 137303.

H. Antil, E. Otárola and A.J. Salgado.
Some applications of weighted norm inequalities to the analysis of PDE constrained optimization problems.
IMA J. Numer. Anal. 38 (2018), no. 2, 852883.

A. Allendes, E. Otárola, R. Rankin and A.J. Salgado.
Adaptive finite element methods for an optimal control problem involving Dirac measures.
Numer. Math. September 2017, Volume 137, Issue 1, pp 159197

E. Otárola and A.J. Salgado.
Optimization of a fractional differential equation.
Frontiers in PDEconstrained Optimization. The IMA Volumes in Mathematics and its Applications

W. Feng, A.J. Salgado, C. Wang and S. Wise.
Preconditioned Steepest Descent Methods for some Nonlinear Elliptic Equations Involving pLaplacian Terms.
J. Comput. Phys., Volume 334, 1 April 2017, Pages 4567.

R.H. Nochetto, A.J. Salgado and I. Tomas.
The equations of ferrohydrodynamics: modeling and numerical methods.
M3AS, Volume 26, Issue 13, 15 December 2016.

R.H. Nochetto, A.J. Salgado and I. Tomas.
A diffuse interface model for twophase ferrofluid flows.
Computer Methods in Applied Mechanics and Engineering. Volume 309, 1 September 2016, Pages 497531.

E. Otárola and A.J. Salgado.
Finite element approximation of the parabolic fractional obstacle problem.
SIAM J. Numer. Anal., 54(4), 2619–2639.

S. Lee, A.J. Salgado.
Stability analysis of pressure correction schemes for the NavierStokes equations with traction boundary conditions.
Computer Methods in Applied Mechanics and Engineering. Volume 309, 1 September 2016, Pages 307324.

H. Antil, E. Otárola and A.J. Salgado.
A spacetime fractional optimal control problem: analysis and discretization.
SIAM J. Control Optim., 54(3), 12951328, 2016.

R.H. Nochetto, E. Otárola and A.J. Salgado.
A PDE approach to spacetime fractional parabolic problems.
SIAM J. Numer. Anal., 54(2), 848873, 2016.

V.J. Ervin, Hyesuk Lee and A.J. Salgado.
Generalized Newtonian fluid flow through a porous medium.
Journal of Mathematical Analysis and Applications, Volume 433, Issue 1, 1 January 2016, Pages 603621.

L. Chen, R.H. Nochetto, E. Otárola and A.J. Salgado.
Multilevel methods for nonuniformly elliptic operators and fractional diffusion.
Math. Comp. 85 (2016), no. 302, 25832607.

R.H. Nochetto, E. Otárola and A.J. Salgado.
Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications.
Numer. Math., January 2016, Volume 132, Issue 1, pp 85130

H. Antil and A.J. Salgado.
Approximation of elliptic equations with BMO coefficients.
IMA J. Numer. Analysis, (2016) 36 (1): 222237.

L. Chen, R.H. Nochetto, E. Otárola and A.J. Salgado.
A PDE approach to fractional diffusion: a posteriori error analysis.
J. Comput. Phys, 2015. Special Issue "Fractional PDEs  Theory, Numerics, and Applications". Volume 293, 15 July 2015, Pages 339358.

R.H. Nochetto, E. Otárola and A.J. Salgado.
Convergence rates for the classical, thin and fractional elliptic obstacle problems.
Philos. Trans. A 373 (2015), no. 2050, 20140449

A.J. Salgado.
Convergence analysis of a fractional timestepping technique for incompressible fluids with microstructure.
J. Sci. Comp., Volume 64, Issue 1, pp 216233, 2015.

R.H. Nochetto, E. Otárola and A.J. Salgado.
A PDE approach to fractional diffusion in general domains: a priori error analysis.
Found. Comp. Math. Volume 15, Issue 3, pp 733791, June 2015.

S. Bartels, R.H. Nochetto and A.J. Salgado.
A total variation diminishing interpolation operator and applications.
Math. Comp., Volume 84, Number 296, November 2015, Pages 25692587.

S. Bartels, R.H. Nochetto and A.J. Salgado.
Discrete total variation flows without regularization.
SIAM J. Numer. Anal., 52(1), 363385. 2014.

R.H. Nochetto, A.J. Salgado and I. Tomas.
The micropolar NavierStokes equations: A priori error analysis.
M3AS. Vol 24, No. 7 (2014) 12371264.

A.J. Salgado.
A framework for the implementation of coupled multiphase flow problems using the
deal.II library and its application to electrowetting.
Archive of Numerical Software 1(2), 119, 2013.

R.H. Nochetto, A.J. Salgado and S.W. Walker.
A diffuse interface model for electrowetting with moving contact lines.
M3AS, Vol. 24, No. 1 (2014) 67111.

J. Guzmán, F.J. Sayas and A.J. Salgado.
A note on the LadyzenskajaBabuskaBrezzi condition.
Journal of Scientific Computing, (2013) 56:219229.

A.J. Salgado.
A diffuse interface fractional timestepping technique for incompressible
twophase flows with moving contact lines.
M2AN Math. Model. Numer. Anal. 47 (2013), no. 3, 743769.

J.L. Guermond, P.D. Minev and A.J. Salgado.
Convergence analysis of a class of massively parallel direction splitting
algorithms for the NavierStokes equations.
Math. Comp. 81 (2012), no. 280, 19511977.

J.L. Guermond, A.J. Salgado.
Error analysis of a fractional timestepping technique for incompressible flows with
variable density.
SIAM J. Numer. Anal. 49(3), pp. 917944.

J.L. Guermond, A. Salgado.
A note on the Stokes operator and its powers.
Journal of Applied Mathematics and Computing.
Volume 36, Numbers 12, 241250.

V. Girault, F. Murat, A. Salgado.
Finite element discretization of Darcy's equations with pressure
dependent porosity.
M2AN Math. Model. Numer. Anal. 44 (2010), no. 6, 11551191..

J.L. Guermond, A. Salgado.
A fractional step method based on a pressure Poisson equation for incompressible
flows with variable density.
J. Comput. Phys. 228 (2009) 28342846.

J.L. Guermond, A. Salgado.
A fractional step method based on a pressure Poisson equation for incompressible
flows with variable density.
C. R. Acad. Sci., Ser. I, 346 (2008) 913918.

V.G. Korneev, S.V. Poborchii, A. Salgado.
Interface Schur complement preconditioning for orthotropic discretizations with high aspect ratios.
In V.G. Korneev (editor) Fast mesh methods of computational continuum mechanics.
Saint Petersburg State University, 2007.

A. Salgado.
Numerical solution of the contact problem of a turbine blade shank.
In V.G. Korneev (editor) Fast mesh methods of computational continuum mechanics.
Saint Petersburg State University, 2007.

A. Salgado.
About the simplifcation of the quasiuniformity conditions for elements associated with a cube.
In V.G. Korneev (editor) Fast mesh methods of computational continuum mechanics.
Saint Petersburg State University, 2007. [Russian].

A. Salgado.
Verification of the approximation estimates for quadrilateral isoparametric finite elements.
In Proceedings of the XXXIII Science week of SPbGPU. Part IV. SPbGPU, 2005. [Russian].
Other

R.H. Nochetto, E. Otárola and A.J. Salgado.
A PDE approach to numerical fractional diffusion.
Proceedings of the ICIAM, Beijing, China. CSIAM, 2015.
arXiv

A.J. Salgado.
Approximation Techniques for Incompressible Flows with Heterogeneous Properties.
PhD Dissertation, Texas A& M University, 2010.

The step35 tutorial program of the deal.II library.
A projection solver for the NavierStokes equations.
