University of Tennessee

Abner J. Salgado


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Publications

Preprints

  1. 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 arXiv
  2. L. Banjai, J.M. Melenk, R.H. Nochetto, E. Otárola, A.J. Salgado and Ch. Schwab. Tensor FEM for spectral fractional diffusion arXiv
  3. H. Antil, E. Otárola and A.J. Salgado. Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects. arXiv
  4. A. Allendes, E. Otárola, R. Rankin and A.J. Salgado. An a posteriori error analysis for an optimal control problem with point sources. arXiv
  5. A.J. Salgado and W. Zhang. Finite element approximation of the Isaacs equation. arXiv

Published or Accepted for Publication

  1. A. Bonito, J.P. Borthagaray, R.H. Nochetto, E. Otárola and A.J. Salgado. Numerical methods for fractional diffusion. Computing and Visualization in Science, 2017 (accepted). arXiv
  2. E. Otárola and A.J. Salgado. Sparse optimal control for fractional diffusion. Computational Methods in Applied Mathematics, 2017 (accepted). DOI: 10.1515/cmam-2017-0030
  3. M. Neilan, A.J. Salgado and W. Zhang. Numerical analysis of strongly nonlinear PDEs. Acta Numerica, Volume 26 2017, pp. 137-303.
  4. 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. Analysis, 2017 (accepted). DOI: 10.1093/imanum/drx018
  5. 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
  6. 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 pdf
  7. 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.
  8. 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.
  9. 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.
  10. E. Otárola and A.J. Salgado. Finite element approximation of the parabolic fractional obstacle problem. SIAM J. Numer. Anal., 54(4), 2619–2639.
  11. 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.
  12. 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.
  13. 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.
  14. 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
  15. 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.
  16. 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.
  17. 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
  18. H. Antil and A.J. Salgado. Approximation of elliptic equations with BMO coefficients. IMA J. Numer. Analysis, (2016) 36 (1): 222-237.
  19. 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.
  20. 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
  21. 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.
  22. 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.
  23. 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.
  24. S. Bartels, R.H. Nochetto and A.J. Salgado. Discrete total variation flows without regularization. SIAM J. Numer. Anal., 52(1), 363-385. 2014.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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. Math. Comp. 81 (2012), no. 280, 1951-1977.
  31. 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.
  32. 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.
  33. 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..
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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].
  39. 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

  1. A.J. Salgado. Approximation Techniques for Incompressible Flows with Heterogeneous Properties. PhD Dissertation, Texas A& M University, 2010.
  2. The step-35 tutorial program of the deal.II library. A projection solver for the Navier-Stokes equations.