Submitted or Accepted

    1. Antil, Harbir; Brown, Thomas S.; Sayas, Francsico-Javier. A problem in control of elastodynamics with piezoelectric effects. Submitted. preprint @ arXiv
    2. Qiu, Tianyu; Rieder, Alexander; Says, Francisco-Javier; Zhang, Shougui. Time-domain boundary integral equation modeling of heat transmission problems. Numer. Math. (in revision) preprint @ arXiv
    3. Hsiao, George C.; Sanchez-Vizuet, Tonatiuh; Sayas, Francisco Javier; Weinacht, Richard. A time-dependent wave-thermoelastic solid interaction. To appear in IMA J. Numerical Analysis.
    4. Sayas, Francisco-Javier.  From Raviart-Thomas to HDG.
      preprint @ arXiv.

Publications

    1. Brown, Thomas S; Sanchez-Vizuet, Tonatiuh; Sayas, Francisco Javier. Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid. To appear in ESAIM Math. Model. Numer. Anal. 52 (2018) 423-455. paper
    2. Brown, Thomas S.; Du, Shukai; Eruslu, Hasan; Sayas, Francisco-Javier. Analysis of models for viscoelastic wave propagation. Appl. Math. Nonlinear Sci. 3 (2018) 55-96. paper
    3. Cockburn, Bernardo; Fu, Zhixing; Hungria, Allan; Ji, Liangyue; Sanchez, Manuel A.; Sayas, Francisco-Javier. Stormer-Numerov HDG methods for acoustic waves. J. Sci. Comput. 75 (2018) 597-624. paper 
    4. Bacuta, Constantin; Jacavage, Jacob; Qirko, Klajdi; Sayas, Francisco-Javier.  Saddle point least squares iterative solvers for the time harmonic Maxwell equations. Comput. Math. Appl. 74 (2017) 2752-2768. paper
    5. Hungria, Allan; Prada, Daniele; Sayas, Francisco-Javier. HDG methods for elastodynamics.  Comput. Math. Appl. 74 (2017) 2617-2690. paper
    6. Fu, Zhixing; Heuer, Norbert; Sayas, Francisco-Javier. A non-symmetric coupling og boundary elements with the Hybridyzable Discontinuous Galerkin method. Comput. Math. Appl. 74 (2017) 2752-2768. paper
    7. Sayas, Francisco-Javier. The mathematical and numerical life of the single layer potential, from Coulomb to Huygens. Rev. R. Acad. Cienc. Exactas Fis. Quim. Nat. Zaragoza. 41 (2017) 11-36. paper
    8. Domínguez, Víctor; Salles, Nicolas; Sayas, Francisco-Javier. Recent progress in time domain boundary integral equations. J. Integral Equations Appl. 29 (2017) 1-4.
      paper
    9. Hassell, Matthew E.; Qiu, Tianyu; Sanchez-Vizuet, Tonatiuh; Sayas, Francisco-Javier. A new and improved analysis of the time domain boundary integral operators for acoustics.  J. Integral Equations Appl. 29 (2017) 107-136.
      paper
    10. Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco-Javier. Superconvergence by M-decompositions. Part I: General theory of HDG methods for diffusion. Math. Comp. 86 (2017) 1609-1641.
      paper
    11. Sanchez-Vizuet, Tonatiuh; Sayas, Francisco-Javier. Boundary-Finite Element discretization of time dependent acoustic scattering by elastic obstacles with piezoelectric behavior.  J. Sci. Comput. 70 (2017) 1290-1315.
      paper
    12. Erath, Christoph; Of, Günther; Sayas, Francisco-Javier.  A non-symmetric coupling of the finite volume method and the boundary element method. Numer. Math. 135 (2017) 895-922. 
      paper
    13. Qiu, Tianyu; Sayas, Francisco-Javier.  New mapping properties of the Time Domain Electric Field Integral Equation.  ESAIM Math. Model. Numer. Anal 51 (2017) 1-15. 
      paper
    14. Hsiao, George C.; Sanchez-Vizuet, Tonatiuh; Sayas, Francisco-Javier. Boundary and coupled boundary-finite element methods for transient wave-structure interaction. IMA J. Numer. Anal. 37 (2017) 237-265.                                                                                             
      paper  
    15. Hsiao, George.C.; Sayas, Francisco-Javier; Weinacht, Richard.J  Time-dependent fluid-structure interaction.  Math. Meth. Appl. Sci. 40 (2017)  486-500.
      paper
    16. Sayas, Francisco-Javier. Retarded potentials and time domain boundary integral equations. A road map. Springer Series in Computational Mathematics, 50. Springer 2016. xv+242 pp. ISBN: 978-3-319-26643-5; 978-3-319-26645-9.
      book
    17. Hassell, Matthew; Sayas, Francisco-Javier. Convolution quadrature for wave simulations. In: Numerical Simulation in Physics and Engineering, 71-159, SEMA-SMAI Springer Series 9, Springer, 2016.
      paper
    18. Heuer, Norbert.; Medahhi, Salim; Sayas, Francisco-Javier  Symmetric Coupling of LDG-FEM and DG-FEM. J Sci Comput 68 (2016) 303-325.
      paper
    19. Ainsworth, Mark; Guzman, Johnny; Sayas, Francisco-Javier. Discrete Extension Operators for Mixed finite element spaces on locally refined meshes.  Math. Comp. 85 (2016) 2639-2650.
      paper
    20. Qiu, Tianyu; Sayas, Francisco-Javier. The Costabel-Stephan system of Boundary Integral Equations in the Time Domain. Math. Comp. 85 (2016) 2341-2364
      paper.
    21. Gatica, Gabriel N.; Hsiao, George C.; Meddahi, Salim; Sayas, Francisco-Javier. New developments on the coupling of mixed-FEM and BEM for the three-dimensional Stokes problem. Int J. Numer. Anal. Model. 13 (2016) 457-492
      paper
    22. Hassell, Matthew E.; Sayas, Francisco-Javier. A fully discrete BEM-FEM scheme for transient acoustic waves.  Comput. Methods Appl. Mech. Engrg. 309 (2016) 106-130.
      paper
    23. Fu, Zhixing; Gatica, Luis F.; Sayas, Francisco-Javier. Algorithm 949: MATLAB tools for HDG in three dimensions. ACM Trans. Math. Software 41 (2015), no. 3, Art. 20, 21 pp. 65-04.
      paper
    24. Domínguez, Víctor; Sánchez-Vizuet, Tonatiuh; Sayas, Francisco-Javier.  A fully discrete Calderón calculus for the two-dimensional elastic wave equation.   Comput. Math. Appl. 69 (2015), no. 7, 620–635.
      paper
    25. Banjai, L.; Lubich, C.; Sayas, F.J. Stable numerical coupling of exterior and interior problems for the wave equation. Numer. Math. 129 (2015), no. 4, 611-646.
      paper
    26. Heuer, Norbert; Sayas, Francisco-Javier. Analysis of a non-symmetric coupling of interior penalty DG and BEM. Math. Comp. 84 (2015), no. 292, 581–598.
      paper
    27. Márquez, Antonio; Meddahi, Salim; Sayas, Francisco-Javier. Strong coupling of finite element methods for the Stokes-Darcy problem. IMA J. Numer. Anal. 35 (2015), no. 2, 969–988.
      paper
    28. Banjai, Lehel; Laliena, Antonio R.; Sayas, Francisco-Javier. Fully discrete Kirchhoff formulas with CQ-BEM. IMA J. Numer. Anal. 35 (2015), no. 2, 859–884.
      paper
    29. Bacuta, Constantin; Hassell, Matthew E.; Hsiao, George C.; Sayas, Francisco-Javier.  Boundary integral solvers for an evolutionary exterior Stokes problem. SIAM J. Numer. Anal. 53 (2015), no. 3, 1370-1392.
      paper
    30. Cockburn, Bernardo; Sayas, Francisco-Javier. Divergence-conforming HDG methods for Stokes flows. Math. Comp. 83 (2014), no. 288, 1571–1598.
      paper
    31. Domínguez, Víctor; Lu, Sijiang L.; Sayas, Francisco-Javier. A Nyström method for the two dimensional Helmholtz hypersingular equation. Adv. Comput. Math. 40 (2014), no. 5-6, 1121–1157.
      paper
    32. Sayas, F.J.; Selgas, V. Variational views of stokeslets and stresslets. SeMA J. (2014) 65-90. paper
    33. Heuer, N.; Karkulik, M.; Sayas, F.J. Note on discontinuous trace approximation in the practical DPG method. Comput. Math. Appl. 68 (2014), no. 11, 1562–1568.
      paper
    34. Domínguez, V.; Sayas, F.J. Some properties of layer potentials and boundary integral operators for the wave equation. J. Int. Equations Appl 25 (2013) 253-294 
      preprint @ arXiv      .
      paper
    35. Marquez, A.; Meddahi, S.; Sayas, F.J. A decoupled preconditioning technique for a mixed Stokes-Darcy model. J. Sci. Comput. 57 (2013) 175-192.
      paper
    36. Bruno, O.; Domínguez, V.; Sayas, F.J. Convergence analysis of a high-order Nystrom integral equation method for surface scattering problems.  Numer. Math. 124 (2013) 603-645
      preprint @ arXiv      .
      paper
    37. Lindsay, A.; Lega, J.; Sayas, F.J. The quenching set of a MEMS capacitor in two dimension al geometries. J. Nonlinear Sci. 23 (2013) 807-834.
      paper
    38. Guzman, J.; Salgado, A.; Sayas, F.J. A note on the Ladyzhenskaya-Babuska-Brezzi condition. J. Sci. Comput. 56 (2013) 219-229.
      paper
    39. Gatica, G.; Meddahi, S.; Hsiao, G.C.; Sayas, F.J. On the dual-mixed formulation for an exterior Stokes problem. ZAMM 93 (2013) 437-445.
      paper
    40. Sayas, F.J. Energy estimates for Galerkin semidiscretization of time domain boundary integral equations. Numer. Math.124 (2013) 121-149
      paper
    41. Sayas, F.J. The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM Review 55 (2013) 131-146
      paper
    42. Cockburn, B.; Guzman, J.; Sayas, F.J. Coupling of Raviart-Thomas and Hybridizable Discontinuous Galerkin Methods with BEM. SIAM J. Numer. Anal. 50 (2012) 2778-2801.
      paper
    43. Bustinza, R.; Sayas, F.J. Error estimates for an LDG method applied to Signorini type problems. J. Sci. Comput. 52 (2012) 322-339.
      paper
    44. Cockburn, B.; Sayas, F.J. The devising of symmetric couplings of boundary element and discontinuous Galerkin methods. IMA J. Numer. Anal. 32 (2012) 765-794.
      paper
    45. Gatica, G.N.; Oyarzúa, R.; Sayas, F.J. A twofold saddle point approach for the coupling of fluid flow with nonlinear porous media flow. IMA J. Numer. Anal. 32 (2012) 845-887.
      paper
    46. Cockburn, B.; Sayas, F.J.; Solano, M. Coupling at a distance HDG and BEM. SIAM J. Sci. Comput. 34 (2012) A28-A47.
      paper
    47. Gatica, G.N.; Hsiao, G.C.; Sayas, F.J. Relaxing the hypotheses of Bielak-MacCamy's BEM-FEM coupling. Numer. Math. 120 (2012) 465-487.
      paper
    48. Gatica, G.N.; Oyarzúa, R.; Sayas, F.J. Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem. Math. Comput. 80 (2011) 1911-1948.
      paper
    49. Gatica, G.N.; Oyarzúa, R.; Sayas, F.J. A residual-based a posteriori error estimator for a fully-mixed formulation of the Stokes-Darcy coupled problem. CMAME 200 (2011) 1877-1891.
      paper
    50. Domínguez, V.; Heuer, N.; Sayas, F.J. Hilbert scales and Sobolev spaces defined by associated Legendre functions. J. Comput Appl. Math. 235 (2011) 3481-2501.
      paper
    51. Cockburn, B.; Gopalakrishnan, J.; Nguyen, N.C.; Peraire, J.; Sayas, F.J. Analysis of HDG methods for Stokes flow. Math. Comput. 80 (2011) 723-760.
      paper
    52. Meddahi, S.; Sayas, F.J.; Selgas, V.  Non-symmetric coupling of BEM and mixed FEM on polyhedral interfaces. Math. Comput. 80 (2011) 43-68.
      paper
    53. Gatica, G.N.; Oyarzúa, R.; Sayas, F.J. Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem. Numer. Methods PDE 27 (2011) 721-748.
      paper
    54. Cockburn, B.; Gopalakrishnan, J.; Sayas, F.J. A projection-based error analysis of HDG methods. Math. Comput. 79 (2010) 1351-1367.
      paper
    55. Gatica, G.N.; Heuer, N.; Sayas, F.J. A direct coupling of local discontinuous Galerkin and boundary element methods. Math. Comput.79 (2010) 1369-1394.
      paper
    56. Sayas, F.J. The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J. Numer. Anal.47 (2009) 3451-3463.
      paper
    57. Laliena, A.R.; Rapún, M.L.; Sayas, F.J. Symmetric boundary integral formulations for Helmholtz transmission problems. Appl. Numer. Math.59 (2009) 2814-2823.
      paper
    58. Jeon, Y.; Sayas, F.J. The CBE-BEM coupling for elliptic problems. Appl. Numer. Math.59 (2009) 2374-2387.
      paper
    59. Laliena, A.R.; Sayas, F.J. A distributional version of Kirchhoff's formula. J. Math. Anal. Appl. 359 (2009) 197-208.
      paper
    60. Laliena, A.R.; Sayas, F.J. Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves. Numer. Math. 112 (2009) 637-678.
      paper
    61. Heuer, N.; Sayas, F.J. Crouzeix-Raviart Boundary Elements. Numer. Math.112 (2009) 381-401.
      paper
    62. Domínguez, V.; Sayas, F.J. Algorithm 884: A simple MATLAB implementation of the Argyris element. ACM Trans. Math. Software 35 (2008) Article 16.
      paper
    63. Boal, N.; Domínguez, V.; Sayas, F.J. Asymptotic properties of some triangulations of the sphere. J. Comput. Appl. Math. 211 (2008) 11-22.
      paper
    64. Bustinza, R.; Gatica, G.N.; Sayas, F.J. On the coupling of Local Discontinuous Galerkin and Boundary Element Methods for nonlinear exterior transmission problems. IMA J. Numer. Anal.28 (2008) 225-244.
      paper
    65. Domínguez, V; Rapún, M.L.; Sayas, F.J. Dirac delta methods for Helmholtz transmission problems. Adv. Comput. Math. 28 (2008) 119-139.
      paper
    66. Gatica, G.N.; Sayas, F.J. Characterising the inf-sup condition on product spaces. Numer. Math.109 (2008) 209-231.
      paper
    67. Rapún, M.L.; Sayas, F.J. Mixed boundary integral methods for Helmholtz transmission problems. J. Comput. Appl. Math  214 (2008) 238-258. 
      paper
    68. Rapún, M.L.; Sayas, F.J. Exterior Dirichlet and Neumann problems for the Hemholtz equation as limits of transmission problems. Integral Methods in Science and Engineering. Techniques and Applications. (Constanda, C.; Potapenko, S., eds) Birkhauser, Boston (2008) 207--216.
      paper
    69. Sayas, F.J. Direct Boundary Element Method with discretization of all integral operators. Integral Methods in Science and Engineering. Techniques and Applications. (Constanda, C.; Potapenko, S., eds) Birkhäuser, Boston (2008) 217-226.
      paper
    70. Bustinza, R.; Gatica, G.N.; Sayas, F.J. A look at how LDG and BEM can be coupled. ESAIM: Proceedings 21 (2007) 88-97.
      paper
    71. Domínguez, V.; Sayas, F.-J. Overlapped BEM-FEM for some Helmholtz transmission problems. Appl. Numer. Math. 57 (2007) 131-146.
      paper
    72. Hohage, T.; Rapún, M.L.; Sayas, F.J. Detecting corrosion using thermal measurements. Inverse Problems 23 (2007) 53-72.
      paper
    73. Rapún, M.L.; Sayas, F.J. Boundary Element Simulation of Thermal Waves. Arch. Comput. Methods Engrg. 14 (2007) 3-46.
      paper
    74. Sayas, F.J. Infimum-supremum. Boletín SEMA, 41 (2007) 19-40.
    75. Bustinza, R.; Gatica, G.N.; Sayas, F.J. A LDG-BEM coupling for a Class of Nonlinear Exterior Transmission Problems. Proceedings of ENUMATH 2005, (Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P. eds) Springer (2006) 1129-1136.
      paper
    76. Domínguez, V.; Sayas, F.-J. A BEM-FEM overlapping algorithm for the Stokes equation. Appl. Math. Comput. 182 (2006) 691-710.
      paper
    77. Gatica G.N.; Sayas, F.J. A note on the local approximation properties of piecewise polynomials with applications to LDG methods. Compl. Var. Ellip. Problems 51 (2006) 101-117.
      paper
    78. Gatica G.N.; Sayas, F.J. An a-priori error analysis for the coupling of local discontinuous Galerkin and boundary element methods. Math. Comput. 75 (2006) 1675-1696.
      paper
    79. Hauke, G.; Doweidar, M.H.; Fuster, D.; Gómez, A.; Sayas, J. Application of Variational a-Posteriori Multiscale Error Estimation to Higher-Order Elements. Comput. Mech. 38 (2006) 356-389.
      paper
    80. Meddahi, S.; Sayas, F.J. BEM-FEM coupling for wave-structure interaction. Scientia. Series A: Math. Sci. 13 (2006) 5-12.
    81. Rapún, M.L.; Sayas, F.J. Boundary integral approximation of a heat-diffusion problem in time-harmonic regime. Numer. Algorithms 41 (2006) 127-160.
      paper
    82. Rapún, M.L.; Sayas, F.J. A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media. ESAIM: M2AN. Math. Model. Numer. Anal. 40 (2006) 871-896.
      paper
    83. Rapún, M.L.; Sayas, F.J. Indirect methods with Brakhage-Werner potentials for Helmholtz transmission problems, Proceedings of ENUMATH 2005, (Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P. eds) Springer (2006) 1146-1154.
    84. Hohage, T.; Sayas, F.J. Numerical solution of a heat diffusion problem by boundary elements using the Laplace transform. Numer. Math 102 (2005) 67-92.
      paper
    85. Meddahi, S.; Sayas, F.J. Analysis of a new BEM-FEM coupling for two dimensional fluid-solid interaction. Numer. Methods Partial Differential Equations 21 (2005) 1017-1154.
      paper
    86. Boal, N; Sayas, F.-J. Adaptive numerical integration on spherical triangles. VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques (Jaca, 2003). Monografías Sem. Mat. G. Galdeano 31, (2004) 61-70.
    87. Celorrio, R; Domínguez, V.; Sayas, F.J. Overlapped BEM-FEM and some Schwarz iterations. Comput. Methods Appl. Math 4 (2004) no. 1, 3-22.
    88. Celorrio, R; Rapún, M.L.; Sayas, F-J. A mixed BEM applied to scattering of thermal waves in composite materials. Integral methods in science and engineering (Saint Étienne, 2002), 31-36, Birkhäuser Boston, Boston, MA, 2004.
    89. Sayas, F.J. Aubin-Nitsche estimates are equivalent to compact embeddings. BIT 44 (2004) no 2., 287-290.
      paper
    90. Celorrio, R.; Domínguez, V.; Sayas, F.-J. An improved quadrature method for integral equations with logarithmic kernel. Actas de las VII Jornadas Zaragoza-Pau de Matemática Aplicada y Estadística (Jaca, 2001). Monografías Sem. Mat. G. Galdeano 27 (2003) 185-192.
    91. Celorrio, R.; Rapún, M.L.; Sayas, F.-J. An integral method for exterior transmission problems with applications to scattering of thermal waves. Actas de las VII Jornadas Zaragoza-Pau de Matemática Aplicada (Jaca, 2001). Monografías Sem. Mat. G. Galdeano 27 (2003) 193-200.
    92. Domínguez, V; Sayas, F.-J. An asymptotic series approach to qualocation methods. J. Integral Equations Appl. 15 (2) (2003) 113-151.
      paper
    93. Domínguez, V; Sayas, F.J. Stability of discrete liftings. C. R. Math. Acad. Sci. Paris 337 (2003) 805-808.
      paper
    94. Sayas, F.-J. A nodal coupling of finite and boundary elements. Numer. Methods Partial Differential Equations 19 (2003) 555-570.
      paper
    95. Celorrio, R.; Domínguez, V.; Sayas, F.J. An interior-exterior Schwarz algorithm and its convervence. C.R.A.S. Paris Ser I. Math. 334 (10) (2002) 923-926.
      paper
    96. Celorrio, R; Domínguez, V.; Sayas, F.-J. Periodic Dirac delta distributions in the boundary element method. Adv. Comput. Math. 17(3) (2002) 211-236.
      paper
    97. Sayas, F.J. Asymptotic series in the numerical analysis of boundary element methods (Spanish) Bol. SEMA 20 (2002) 77-96.
    98. Celorrio, R; Domínguez, V.; Sayas, F.-J. Asymptotics of finite element Lagrange interpolation under the action of an integral operator. Actes des VI Journées Zaragoza-Pau de Mathématiques Apliquées (Jaca, 1999), 151-158, Université de Pau, 2001.
    99. Celorrio, R.; Sayas, F.-J. Extrapolation techniques and the collocation method for a class of boundary integral equations. ANZIAM J. (formerly J. Austral. Math. Soc. Ser. B/Applied) 42 (2001) 413-437.
      paper
    100. Crouzeix. M; Féat, Ph; Sayas, F.-J. Theoretical and numerical approximation of a free boundary problem by boundary integral methods. M2AN Math. Model. Numer.Anal.35 (2001) no.6, 1137-1158.
      paper
    101. Domínguez, V.; Sayas, F.-J. Full asymptotics of spline Petrov-Galerkin methods for some periodic pseudodifferential equations. Adv. Comput. Math. 14 (1) (2001) 75-101.
      paper
    102. Domínguez, V.; Sayas, F.-J.. Local expansions of periodic spline interpolation with some applications. Math. Nach. 227 (2001) 43-62 .
      paper
    103. Meddahi, S; Sayas, F.-J.. A fully discrete BEM--FEM for the exterior Stokes problem in the plane. SIAM J. Numer. Anal. 37 (2000), no. 6, 2082--2102.
      paper
    104. Celorrio, R; Domínguez, V.; Sayas, F.-J. On the averaged delta method for some acoustic scattering problems. Proceedings of the 6th International Congress on Sound and Vibration, (Copenhagen, 1999), 547-554. IIAV, 1999. 
    105. Celorrio, R. Sayas, F.-J. Full collocation methods for some boundary integral equations. Numer. Algorithms 22 (1999), no. 3-4, 327-351.
      paper
    106. Celorrio, R.; Sayas, F.-J. The Euler-Maclaurin formula in presence of a logarithmic singularity. BIT 39 (1999), no. 4, 780-785.
      paper
    107. Sayas, F.-J. The numerical solution of Symm's equation on smooth open arcs by spline Galerkin methods. Numerical mathematics and computational mechanics (Miskolc, 1996). Comput. Math. Appl. 38 (1999), no. 9-10, 87--99.
      paper
    108. Crouzeix, M.; Sayas, F.-J. Asymptotic expansions of the error of spline Galerkin boundary element methods. Numer. Math. 78 (1998), no. 4, 523-547.
      paper
    109. Sayas, F.-J. A generalized Euler-Maclaurin formula on triangles. J. Comput.Appl. Math. 93 (1998), no. 2, 89--93.
      paper
    110. Sayas, F.-J. Fully discrete Galerkin methods for systems of boundary integral equations. J. Comput. Appl. Math. 81 (1997), no. 2, 311--331.
      paper