# 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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## Books and Monographs

T. Mengesha and A.J. Salgado (Eds.) Proceedings of the 50th Barrett Memorial Lectures: A³N²M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models. IMA Vol. Math. Appl., 165. Springer, 2023.

A.J. Salgado and Steven M. Wise. Classical Numerical Analysis: A Comprehensive Course. Cambridge University Press, 2022.

## Preprints

A.J. Salgado, S.E. Sawyer. A semi-analytic diagonalization FEM for the spectral fractional Laplacian. arXiv

F.R.A. Aznaran, M. Bukac, B. Muha, A.J. Salgado. Analysis and finite element approximation of a diffuse interface approach to the Stokes--Biot coupling. arXiv

J.P. Borthagaray, R.H. Nochetto, A.J. Salgado, C. Torres. Monotone two-scale methods for a class of integrodifferential operators and applications. arXiv

## Published or Accepted for Publication

### Surveys

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

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. 5-6, 19-46.

M. Neilan, A.J. Salgado and W. Zhang. Numerical analysis of strongly nonlinear PDEs. Acta Numerica, Volume 26 2017, pp. 137-303.

### Research articles

A. Kh. Balci, L. Diening, A.J. Salgado. Numerical approximation of variational problems with orthotropic growth. Numer. Math. 156, 1751–1779 (2024).

T. Mengesha, E. Otarola, A.J. Salgado. Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes. Journal of Differential Equations. Volume 412, 15 December 2024, Pages 250-271.

A. Allendes, G. Campana, E. Otarola, A.J. Salgado. The linear elasticity system under singular forces. Applied Math. Letters Volume 158, December 2024, 109258.

L. Diening, J. Rolfes, A.J. Salgado. Pointwise gradient estimate on the Ritz projection. SIAM J. Numer. Anal. Vol 62, No. 3, pp. 1212-1225, 2024.

W. Li and A.J. Salgado. Two-scale methods for the normalized infinity Laplacian: rates of convergence. IMA J. Numer. Anal. 44 (2024), no. 5, 2603–2666.

M. Bukac, B. Muha, A.J. Salgado. Analysis of a diffuse interface method for the Stokes-Darcy coupled problem. ESAIM: M2AN Volume 57, Number 5 (2023), pp. 2623 - 2658.

T. Mengesha, A.J. Salgado, J.M. Siktar. On the Optimal Control of a Linear Peridynamics Model. AMOP 88, Article number: 70 (2023).

W. Li and A.J. Salgado. Time fractional gradient flows: Theory and numerics. M3AS Vol. 33, No. 02, pp. 377-453 (2023).

A.J. Salgado and I. Tomas. Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties. Journal of Numerical Mathematics. 31 (2023), no. 4, 313–341.

J.-H. Park, A.J. Salgado, and S.M. Wise. Benchmark computations of the Phase field crystal and Functionalized Cahn-Hilliard equations via fully implicit, Nesterov accelerated schemes. Communications in Computational Physics, 33 (2023), no. 2, 367–398.

E. Otárola, and A.J. Salgado. On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra. Numerische Mathematik 151, pages185 - 218 (2022). DOI: 10.1007/s00211-022-01272-5.

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. J. Sci. Comput. 89 (2021), no. 1, Paper No. 17, 37 pp.

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. 398 (2021), 113642, 13 pp.

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. 789-827, 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), A1860-A1884.

R.G. Durán, E. Otárola, A.J. Salgado. Stability of the Stokes projection on weighted spaces and applications. Math. Comp. 89 (2020), 1581-1603. 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. 2679-2717 (2019).

A. Bonito, W. Lei, and A.J. Salgado. Finite element approximation of an obstacle problem for a class of integro-differential operators. ESAIM: M2AN, 54 1 (2020) 229-253 .

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. Maximum-norm a posteriori error estimates for an optimal control problem. Computational Optimization and Applications. July 2019, Volume 73, Issue 3, pp 997-1017

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, 2659-2675.

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), 1007-1032.

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 1-2, March 2019, Pages 599-612.

A.J. Salgado and W. Zhang. Finite element approximation of the Isaacs equation. ESAIM: M2AN 53 (2019) 351-374.

E. Otárola and A.J. Salgado. Regularity of solutions to space-time 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, 901-962.

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 204-224. DOI: 10.1007/s10915-018-0703-0

M.A. Olshanskii, L.G. Rebholz and A.J. Salgado. On well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations with no-slip boundary conditions. DCDS, 38(7): 3459-3477, 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, 1617-1650. DOI: 10.1051/m2an/2018010

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

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, 852-883.

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 159-197.

W. Feng, A.J. Salgado, C. Wang and S. Wise. Preconditioned Steepest Descent Methods for some Nonlinear Elliptic Equations Involving p-Laplacian Terms. J. Comput. Phys., Volume 334, 1 April 2017, Pages 45-67.

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 two-phase ferrofluid flows. Computer Methods in Applied Mechanics and Engineering. Volume 309, 1 September 2016, Pages 497-531.

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 Navier-Stokes equations with traction boundary conditions. Computer Methods in Applied Mechanics and Engineering. Volume 309, 1 September 2016, Pages 307-324.

H. Antil, E. Otárola and A.J. Salgado. A space-time fractional optimal control problem: analysis and discretization. SIAM J. Control Optim., 54(3), 1295-1328, 2016.

R.H. Nochetto, E. Otárola and A.J. Salgado. A PDE approach to space-time fractional parabolic problems. SIAM J. Numer. Anal., 54(2), 848-873, 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 603-621.

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, 2583-2607.

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 85-130

H. Antil and A.J. Salgado. Approximation of elliptic equations with BMO coefficients. IMA J. Numer. Analysis, (2016) 36 (1): 222-237.

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 339-358.

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 time-stepping technique for incompressible fluids with microstructure. J. Sci. Comp., Volume 64, Issue 1, pp 216-233, 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 733-791, 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 2569-2587.

S. Bartels, R.H. Nochetto and A.J. Salgado. Discrete total variation flows without regularization. SIAM J. Numer. Anal., 52(1), 363-385. 2014.

R.H. Nochetto, A.J. Salgado and I. Tomas. The micropolar Navier-Stokes equations: A priori error analysis. M3AS. Vol 24, No. 7 (2014) 1237-1264.

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), 1-19, 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) 67-111.

J. Guzmán, F.-J. Sayas and A.J. Salgado. A note on the Ladyzenskaja-Babuska-Brezzi condition. Journal of Scientific Computing, (2013) 56:219-229.

A.J. Salgado. A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines. M2AN Math. Model. Numer. Anal. 47 (2013), no. 3, 743-769.

J.-L. Guermond, P.D. Minev and A.J. Salgado. Convergence analysis of a class of massively parallel direction splitting algorithms for the Navier-Stokes equations in simple domains. Math. Comp. 81 (2012), no. 280, 1951-1977.

J.-L. Guermond, A.J. Salgado. Error analysis of a fractional time-stepping technique for incompressible flows with variable density. SIAM J. Numer. Anal. 49(3), pp. 917-944.

J.-L. Guermond, A. Salgado. A note on the Stokes operator and its powers. Journal of Applied Mathematics and Computing. Volume 36, Numbers 1-2, 241-250.

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, 1155-1191.

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) 2834-2846.

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) 913-918.

### Conference proceedings

E. Otárola and A.J. Salgado. Optimization of a fractional differential equation. Frontiers in PDE-constrained Optimization. The IMA Volumes in Mathematics and its Applications., 163, Springer, New York, 2018.

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 quasi-uniformity 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

Tomas, I. and Shadid, J. and Maier, M. and Salgado, A.J. Asymptotic preserving methods for fluid electron-fluid models in the large magnetic field limit with mathematically guaranteed properties. OSTI Final Report: 2022. doi:10.2172/1872178.

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.

A.J. Salgado. The step-35 tutorial program of the deal.II library. A projection solver for the Navier-Stokes equations.