Submitted or Accepted

    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. Submitted.
      preprint @ arXiv

    2. Hungria, Allan; Prada, Daniele; Sayas, Francisco Javier. HDG methods for elastodynamics. Submitted.
      preprint @ arXiv
    3. Hsiao, George C.; Sanchez-Vizuet, Tonatiuh; Sayas, Francisco Javier; Weinacht, Richard. A time-dependent wave-thermoelastic solid interaction. In revision in IMA J. Numerical Analysis.
      preprint @ arXiv
    4. Cockburn, Bernardo; Fu, Zhixing; Hungria, Allan; Ji, Liangyue; Sanchez, Manuel A.; Sayas, Francisco-Javier. Stormer-Numerov HDG methods for acoustic waves. Submitted
    5. Fu, Zhixing; Heuer, Norbert; Sayas, Francisco Javier. A non-symmetric coupling og boundary elements with the Hybridyzable Discontinuous Galerkin method. Submitted.
    6. Sayas, Francisco-Javier.  From Raviart-Thomas to HDG.
      preprint @ arXiv.
    7. Sayas, Francisco-Javier. The mathematical and numerical life of the single layer potential, from Coulomb to Huygens. To appear in Rev. R. Acad. Cienc. Exactas Fis. Quim. Nat. Zaragoza (2017)

Publications

    1. Domínguez, Víctor; Salles, Nicolas; Sayas, Francisco-Javier. Recent progress in time domain boundary integral equations. J. Integral Equations Appl. 29 (2017) 1-4.
      paper
    2. 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
    3. Cockburn, Bernardo; Fu, Guosheng; Sayas, Francisco-Javier. Superconvergence by M-decompositions. Part I: General theory of HDG methods for diffusion. To appear in Math. Comp.86 (2017) 1609-1641.
      paper
    4. 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
    5. 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
    6. 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
    7. 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  
    8. Hsiao, George.C.; Sayas, Francisco-Javier; Weinacht, Richard.J  Time-dependent fluid-structure interaction.  Math. Meth. Appl. Sci. 40 (2017)  486-500.
      paper
    9. 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
    10. 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
    11. Heuer, Norbert.; Medahhi, Salim; Sayas, Francisco-Javier  Symmetric Coupling of LDG-FEM and DG-FEM. J Sci Comput 68 (2016) 303-325.
      paper
    12. 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
    13. Qiu, Tianyu; Sayas, Francisco-Javier. The Costabel-Stephan system of Boundary Integral Equations in the Time Domain. Math. Comp. 85 (2016) 2341-2364
      paper.
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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
    20. 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
    21. 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
    22. 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
    23. Cockburn, Bernardo; Sayas, Francisco-Javier. Divergence-conforming HDG methods for Stokes flows. Math. Comp. 83 (2014), no. 288, 1571–1598.
      paper
    24. 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
    25. Sayas, F.J.; Selgas, V. Variational views of stokeslets and stresslets. SeMA J. (2014) 65-90. paper
    26. 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
    27. 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

    28. 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

    29. 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
    30. 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
    31. Guzman, J.; Salgado, A.; Sayas, F.J. A note on the Ladyzhenskaya-Babuska-Brezzi condition. J. Sci. Comput. 56 (2013) 219-229.
      paper

    32. 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
    33. Sayas, F.J. Energy estimates for Galerkin semidiscretization of time domain boundary integral equations. Numer. Math.124 (2013) 121-149
      paper

    34. Sayas, F.J. The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM Review 55 (2013) 131-146
      paper

    35. 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

    36. Bustinza, R.; Sayas, F.J. Error estimates for an LDG method applied to Signorini type problems. J. Sci. Comput. 52 (2012) 322-339.
      paper

    37. 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
    38. 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
    39. Cockburn, B.; Sayas, F.J.; Solano, M. Coupling at a distance HDG and BEM. SIAM J. Sci. Comput. 34 (2012) A28-A47.
      paper
    40. 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
    41. 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
    42. 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
    43. 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
    44. 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
    45. 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
    46. 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
    47. Cockburn, B.; Gopalakrishnan, J.; Sayas, F.J. A projection-based error analysis of HDG methods. Math. Comput. 79 (2010) 1351-1367.
      paper
    48. 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
    49. Sayas, F.J. The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J. Numer. Anal.47 (2009) 3451-3463.
      paper
    50. 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
    51. Jeon, Y.; Sayas, F.J. The CBE-BEM coupling for elliptic problems. Appl. Numer. Math.59 (2009) 2374-2387.
      paper
    52. Laliena, A.R.; Sayas, F.J. A distributional version of Kirchhoff's formula. J. Math. Anal. Appl. 359 (2009) 197-208.
      paper
    53. 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
    54. Heuer, N.; Sayas, F.J. Crouzeix-Raviart Boundary Elements. Numer. Math.112 (2009) 381-401.
      paper
    55. Domínguez, V.; Sayas, F.J. Algorithm 884: A simple MATLAB implementation of the Argyris element. ACM Trans. Math. Software 35 (2008) Article 16.
      paper
    56. Boal, N.; Domínguez, V.; Sayas, F.J. Asymptotic properties of some triangulations of the sphere. J. Comput. Appl. Math. 211 (2008) 11-22.
      paper
    57. 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
    58. Domínguez, V; Rapún, M.L.; Sayas, F.J. Dirac delta methods for Helmholtz transmission problems. Adv. Comput. Math. 28 (2008) 119-139.
      paper
    59. Gatica, G.N.; Sayas, F.J. Characterising the inf-sup condition on product spaces. Numer. Math.109 (2008) 209-231.
      paper
    60. Rapún, M.L.; Sayas, F.J. Mixed boundary integral methods for Helmholtz transmission problems. J. Comput. Appl. Math  214 (2008) 238-258. 
      paper
    61. 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
    62. 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
    63. 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
    64. Domínguez, V.; Sayas, F.-J. Overlapped BEM-FEM for some Helmholtz transmission problems. Appl. Numer. Math. 57 (2007) 131-146.
      paper
    65. Hohage, T.; Rapún, M.L.; Sayas, F.J. Detecting corrosion using thermal measurements. Inverse Problems 23 (2007) 53-72.
      paper
    66. Rapún, M.L.; Sayas, F.J. Boundary Element Simulation of Thermal Waves. Arch. Comput. Methods Engrg. 14 (2007) 3-46.
      paper
    67. Sayas, F.J. Infimum-supremum. Boletín SEMA, 41 (2007) 19-40.
    68. 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
    69. Domínguez, V.; Sayas, F.-J. A BEM-FEM overlapping algorithm for the Stokes equation. Appl. Math. Comput. 182 (2006) 691-710.
      paper
    70. 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
    71. 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
    72. 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
    73. Meddahi, S.; Sayas, F.J. BEM-FEM coupling for wave-structure interaction. Scientia. Series A: Math. Sci. 13 (2006) 5-12.
    74. 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
    75. 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
    76. 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.
    77. 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
    78. 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
    79. 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.
    80. Celorrio, R; Domínguez, V.; Sayas, F.J. Overlapped BEM-FEM and some Schwarz iterations. Comput. Methods Appl. Math 4 (2004) no. 1, 3-22.
    81. 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.
    82. Sayas, F.J. Aubin-Nitsche estimates are equivalent to compact embeddings. BIT 44 (2004) no 2., 287-290.
      paper
    83. 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.
    84. 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.
    85. Domínguez, V; Sayas, F.-J. An asymptotic series approach to qualocation methods. J. Integral Equations Appl. 15 (2) (2003) 113-151.
      paper
    86. Domínguez, V; Sayas, F.J. Stability of discrete liftings. C. R. Math. Acad. Sci. Paris 337 (2003) 805-808.
      paper
    87. Sayas, F.-J. A nodal coupling of finite and boundary elements. Numer. Methods Partial Differential Equations 19 (2003) 555-570.
      paper
    88. 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
    89. 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
    90. Sayas, F.J. Asymptotic series in the numerical analysis of boundary element methods (Spanish) Bol. SEMA 20 (2002) 77-96.
    91. 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.
    92. 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
    93. 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
    94. 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
    95. Domínguez, V.; Sayas, F.-J.. Local expansions of periodic spline interpolation with some applications. Math. Nach. 227 (2001) 43-62 .
      paper
    96. 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
    97. 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. 
    98. Celorrio, R. Sayas, F.-J. Full collocation methods for some boundary integral equations. Numer. Algorithms 22 (1999), no. 3-4, 327-351.
      paper
    99. Celorrio, R.; Sayas, F.-J. The Euler-Maclaurin formula in presence of a logarithmic singularity. BIT 39 (1999), no. 4, 780-785.
      paper
    100. 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
    101. 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
    102. Sayas, F.-J. A generalized Euler-Maclaurin formula on triangles. J. Comput.Appl. Math. 93 (1998), no. 2, 89--93.
      paper
    103. Sayas, F.-J. Fully discrete Galerkin methods for systems of boundary integral equations. J. Comput. Appl. Math. 81 (1997), no. 2, 311--331.
      paper