Numerical Methods for Partial Differential and Integral Equations

 

Articles in journals

Work in
Progress
 
  1. Bustinza, R.; Sayas, F.J. Error estimates for an LDG method applied to Signorini type problems. Submitted
  2. Clavero, C.; Gracia, J.L.; Stynes, A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems. Submitted
  3. Cockburn, B.; Sayas, F.J. Divergence-conforming HDG methods for Stokes flow. Submitted.
  4. Gatica, G.N.; Hsiao, G.C.; Sayas, F.J. Relaxing the hypotheses on Bielak-MacCamy's BEM-FEM coupling. Submitted
  5. Gatica, G.N.; Oyarzua, R.; Sayas, F.J. A residual-based a posteriori error estimator for a fully-mixed formulation of the Stokes-Darcy coupled problem. Submitted.
  6. Gatica, G.N.; Oyarzúa, R.; Sayas, F.J. A twofold saddle point approach for the coupling of fluid flow with nonlinear porous media flow. Submitted.
To appear
  1. Boal, N.; Gaspar, F.J.; Lisbona, F.J.; Vabishchevich, P.N. Finite Difference Analysis of a Double Porosity Consolidation Model. Numer. Methods Partial Differential Equations
  2. Cockburn, B.; Gopalakrishnan, J.; Nguyen, N.C.; Peraire, J.; Sayas, F.J. Analysis of HDG methods for Stokes flow. Math. Comput.
  3. Cockburn, B.; Sayas, F.J. The devising of symmetric couplings of boundary element and discontinuous Galerkin methods. IMA J. Numer. Anal.
  4. Domínguez, V.; Graham, I.G.; Smyshlaev, V.P. Stability and error estimates for Filon-Clenshaw-Curtis rules for highly-oscillatory integrals. IMA J. Numer. Anal.
  5. Domínguez, V.; Heuer, N.; Sayas, F.J. Hilbert scales and Sobolev spaces defined by associated Legendre functions. J. Comput. Anal. Appl.
  6. Gaspar F.J.; Lisbona F.J.; Rodrigo C. Multigrid finite element method on semi-structured grids for the poro-elasticity problem. Lecture Notes in Comput. Sci.
  7. Gatica, G.N.; Oyarzúa, R.; Sayas, F.J. Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem. Numer. Methods Partial Differential Equations
  8. Gatica, G.N.; Oyarzúa, R.; Sayas, F.J. Analysis of fully mixed finite element methods for the Stokes-Darcy coupled problem. Math. Comput.

2011
  1. Meddahi, S.; Sayas, F.J.; Selgás, V. Non-symmetric coupling of BEM and mixed FEM on polygonal interfaces. Math. Comput. 80 (2011) 43-68
2010
  1. Apiñaniz, E.; Medioroz, A.; Salazar, A.; Celorrio, R. Analysis of the Tikhonov regularization to retrieve thermal conductivity depth-profiles from infrared thermography. J. Appl. Phys. 108 (2010) Art. Num. 064905
  2. Bawa, R.K.; Clavero, C. Higher Order Global Solution and Normalized flux for Singularly Perturbed Reaction-Diffusion Problems. Appl. Math. Comp. 216 (2010) 2058-2068
  3. Carpio, A.; Johansson, T.; Rapún, M.L. Determining planar multiple sound-soft obstacles from scattered acoustic fields. J. Math. Imaging
    Vision 36 (2010) 185-199
  4. Carpio, A.; Rapún, M.L.  An iterative method for parameter identification and shape reconstruction. Inverse Probl. Sci. Eng. 18 (2010) 35-50
  5. Celorrio, R.; Apiñaniz, E.; Mendioroz, A.; Salazar, A.; Mandelis, A. Accurate reconstruction of the thermal conductivity depth profile in case hardened steel. J. Appl. Phys. (2010) Art. Num. 083519
  6. Clavero, C.; Gracia, J.L. On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems. Appl. Math. Comp. 216 (2010) 1478-1488
  7. Clavero, C.; Gracia, J.L.; Lisbona, F.J. An almost third order finite difference scheme for  singularly perturbed reaction-diffusion systems. J. Comput. Appl. Math. 234 (2010) 2501-2515
  8. Clavero, C.; Gracia, J.L.; Lisbona, F.J. Second order uniform approximations for the solution of time dependent singularly perturbed reaction-difussion systems. International Journal of Numerical Analysis and Modeling 7 (2010) 428-443
  9. Cockburn, B.; Gopalakrishnan, J.; Sayas, F.J. A projection-based error analysis of HDG methods. Math. Comput. 79 (2010) 1351-1367
  10. Gaspar, F.J.; Gracia, J.L.; Lisbona, F.J.; Rodrigo, C. Efficient geometric multigrid implementation for triangular grids. J. Comput. Appl. Math. 234 (2010) 1027-1035
  11. Gaspar, F.J.; Gracia, J.L.; Lisbona, F.J.; Rodrigo, C. Multigrid finite element methods on semi-structured triangular grids for planar elasticity. Numer. Linear Algebra Appl.17 (2010) 473-493
  12. Gaspar F.J.; Lisbona F.J.; Rodrigo C. Multigrid Fourier analysis on semi-structured anisotropic meshes for vector problems. Math. Model. Anal 15 (2010) 39-54
  13. 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
  14. Gracia, J.L.; Lisbona, F.J.; O'Riordan, E. A coupled system of singularly perturbed parabolic reaction-diffusion equations. Adv. Comput. Math. 32 (2010) 43-61
  15. Heidenreich, E.A.; Gaspar, F.J.; Ferrero, J.F.; Rodriguez, J.F. Compact schemes for anisotropic reaction-diffusion equations with adaptive time step. Int. J. Numer. Meth. Eng. 82 (2010) 1022-1043
  16. Rapún, M.L.; Vega, J.M. Reduced order models based on local POD plus Galerkin projection. J. Comput. Phys. 229 (2010) 3046-3063
  17. Rodrigo, C.; Gaspar, F.J.; Oosterlee, C.W.; Yavneh, I. Accuracy measures and Fourier analysis for the full multigrid algorithm. SIAM J. Sci. Comput. 32 (2010) 3108-3129
  18. Salazar, A.; Mendioroz, A.; Fuente, R.; Celorrio, R. Accurate measurements of the thermal diffusivity of thin filaments by lock-in thermography. J. Appl. Phys. 107 (2010) Art. Num. 043508 
2009
  1. Celorrio R.; Mendioroz A.; Apiñaniz E.; Salazar A.; Wang C.; Mandelis A. Reconstruction of radial thermal conductivity depth profile in case hardened steel rods. J. Appl. Phys. 105 (2009) Art. Num. 083517 (1-7)
  2. Clavero, C.; Bawa, R. K.; Natesan, S. A robust second-order numerical method for global solution and global normalized flux of singularly perturbed self-adjoint boundary-value problems. Int. J. Comput. Math., 86, n. 10–11 (2009) 1731-1745.
  3. Clavero, C.; Gracia, J.L.; Lisbona, F.J. High order schemes for reaction-diffusion singularly perturbed systems. Lecture Notes in Comput. Sci. Engineering 69 (2009) 107-115
  4. Gaspar, F.J.; Gracia, J.L.; Lisbona, F.J. Fourier analysis for multigrid methods on triangular grids. SIAM J. Sci. Comput. 31 (2009) 2081-2102
  5. Gaspar, F.J.; Gracia, J.L.; Lisbona, F.J.; Rodrigo, C. On geometric multigrid methods for triangular grids using three-coarsening strategy. Appl. Numer. Math. 59 (2009) 1693-1708
  6. Gracia, J.L.; Lisbona,  F.J.; Madaune-Tort, M.; O'Riordan, E. A system of singularly perturbed semilinear equations. Lecture Notes in Comput. Sci. Engineering 69 (2009) 163-172
  7. Heuer, N.; Sayas, F.J. Crouzeix-Raviart Boundary Elements. Numer. Math. 112 (2009) 381-401
  8. Jeon, Y.; Sayas, F.J. The CBEM-BEM coupling for elliptic problems. Appl. Numer. Math. 59 (2009) 2374-2387
  9. Laliena, A.R.; Rapún, M.L.; Sayas, F.J. Symmetric boundary integral formulations for Helmholtz transmission problems. Appl. Numer. Math. 59 (2009) 2814-2823
  10. Laliena, A.R.; Sayas, F.J. A distributional version of Kirchhoff's formula. J. Math. Anal. Appl. 359 (2009) 197-208
  11. 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
  12. Sayas, F.J. The validity of Johnson-Nedelec's BEM-FEM coupling on polygonal interfaces. SIAM J. Numer. Anal. 47 (2009) 3451-3463
2008
  1. Aguilar G., Gaspar F.J., Lisbona F.J., Rodrigo C. Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation. Int. J. Numer. Meth. Eng. 75 (2008) 1282-1300
  2. Apianiz, E.; Mendioroz, A.; Madariaga, N.; Oleaga, A. ;Celorrio, R.; Salazar, A. Thermal characterization of rods, tubes, and spheres using pulsed infrared thermography. J. Phys. D: Appl. Phys. 41 (2008) art. 015403
  3. Boal, N.; Domínguez, V.; Sayas, F.J. Asymptotic properties of some triangulations of the sphere. J. Comput. Appl. Math. 211 (2008) 11-22.
  4. 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.
  5. Carpio, A.; Rapún, M.L. Solving inhomogeneous inverse problems by topological derivative methods. Inverse Problems 24 (2008)
  6. Carpio, A.; Rapún, M.L. Domain reconstruction using photothermal techniques. J. Comput. Phys. 227 (2008) 8083-8106
  7. Celorrio, R.; Costa, M.; Mendioroz, A.; Apiñaniz, E.; Shibli, S.M.; Salazar, A. Thermal Wave Scattering by Two Overlapping and Parallel Cylinders. Applied Physics A: Material Sciences & Processing (2008) 1-9.
  8. Celorrio, R.; Hofinger, A.: A real-time solution for an inverse Cauchy problem in cardiology. Inverse Probl. Sci. Eng. 16 (2008) 281-301
  9. Ciegis, R.; Gaspar, F.J., Rodrigo C. On the parallel multiblock geometric multigrid algorithm. CMAM 8 (2008) 223-236.
  10. Domínguez, V; Rapún, M.L.; Sayas, F.J. Dirac delta methods for Helmholtz transmission problems. Adv. Comput. Math. 28 (2008) 119-139
  11. Domínguez, V.; Sayas, F.J. Algorithm 884: A simple MATLAB implementation of the Argyris element. ACM Trans. Math. Software. 35 (2008)
  12. Gaspar, F.J.; Gracia, J.L.; Lisbona, F.J.; Oosterlee, C.W. Distributive Smoothers in Multigrid for Problems with Dominating Grad-Div Operators. Numer. Linear Algebra Appl. 15 (2008) 661-683.
  13. Gaspar, F.J; Gracia, J.L.; Lisbona, L.;Vabishchevich, P.N. A stabilized method for a secondary consolidation Biot's model. Numer. Methods Partial Differential Equations 24 (2008) 60-78.
  14. Gaspar F.J.; F. Lisbona, F; Oosterlee, C.W. A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods. Comput. Vis. Sci. 11 (2008) 67-76
  15. Gatica, G.N.; Sayas, F.J. Characterising the inf-sup condition on product spaces. Numer. Math. 109 (2008) 209-231
  16. Heidenreich E., Rodriguez J.F., Gaspar F.J., Doblaré M. Fourth Order Compact Schemes for Monodomain Reaction Diffusion Equations. J. Comput. Appl. Math. 216 (2008) 39-55
  17. Naumovich, A.; Gaspar, F.J. On a multigrid solver for the three-dimensional Biot poroelasticity system in multilayered domains. Comput. Vis. Sci. 11 (2008) 77-87
  18. Oosterlee C.W., Gaspar, F.J. Multigrid relaxation methods for systems of saddle point type. Appl. Numer. Math.58 (2008) 1933-1950.
  19. Rapún, M.L.; Sayas, F.J. Mixed boundary integral methods for Helmholtz transmission problems. J. Comput. Appl. Math  214 (2008) 238-258
  20. Salazar, A; Celorrio, R. Propagation of thermal waves in multilayered cylinders using the thermal quadrupole method. The European Physical Journal - Special Topics (Formerly, Journal de Physique I) 153 (2008) 383-386
2007
  1. Bujanda, B.; Clavero, C; Gracia, J.L.; Jorge, J.C. A high order uniformly convergent alternating direction scheme for time dependent reaction-diffusion singularly perturbed problems. Numer. Math. 107 (2007) 1-25.
  2. Domínguez, V.; Sayas, F.-J. Overlapped BEM-FEM for some Helmholtz transmission problems. Appl. Numer. Math. 57 (2007) 131-146
  3. Domínguez, V.; Graham, I.G.; Smyshlyaev, V.P. A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Numer. Math. 106 (2007) 471-510.
  4. Gaspar, F.J.; Lisbona, F.J.; Oosterlee, C.W., Vabishchevich, P.N An efficient multigrid solver for a reformulated version of the poroelasticity system.  Comput. Methods Appl. Mech. Engrg. 196 (2007) 1447-1457.
  5. Gracia, J.L.; Lisbona, F.J. A uniformly convergent scheme for a system of reaction-diffusion equations. J. Comput. Appl. Math. 206 (2007) 1-16.
  6. Hohage, T.; Rapún, M.L.; Sayas, F.J. Detecting corrosion using thermal measurements. Inverse Problems 23 (2007) 53-72
  7. Natesan, S.; Bawa, R.K.; Clavero, C. Uniformly convergent compact numerical scheme for the normalized flux of singularly perturbed reaction-diffusion problems, Int. J. Inf. Syst. Sci.,  3 (2007) 207-221
  8. Rapún, M.L.; Sayas, F.J. Boundary Element Simulation of Thermal Waves. Arch. Comput. Methods Engrg. 14 (2007) 3-46
  9. Sayas, F.J. Infimum-supremum. Boletín SEMA, 41 (2007) 19-40.
2006
  1. Aguilar, G.; Lévi, L.; Madaune-Tort, M. Coupling of multidimensional parabolic and hyperbolic equations. J. Hyperbolic Differ. Equ. 3 (2006) 53-80.
  2. Clavero, C; Gracia, J.L.; Jorge, J.C. A Uniformly Convergent Alternating Direction HODIE Finite Difference Scheme for 2D Time Dependent Convection-Diffusion Problems. IMA J. Numer. Anal. 26 (2006) 155-172
  3. Domínguez, V.; Sayas, F.-J A BEM-FEM overlapping algorithm for the Stokes equation. Appl. Math. Comput. 182 (2006) 691-710
  4. Gaspar F.J.; Lisbona, F.J.; Vabishchevich,P.N. Staggered grid discretizations for the quasi-static Biot's consolidation problem. Appl. Num. Math. 56 (2006) 888-898.
  5. 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
  6. 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
  7. Gracia, J.L;, Clavero, C, A compact finite difference scheme for 2D reaction-diffusion singularly perturbed problems. J. Comput. Appl. Math.192 (2006) 152-167
  8. Gracia, J.L.; O'Riordan, E. A defect-correction parameter-uniform method for a singularly perturbed convection-diffusion problem in one dimension.  Numer. Algorithms 41 (2006) 359-385.
  9. Gracia, J.L.; O'Riordan, E.; Pickett, M.L. A parameter robust higher order numerical method for a singularly perturbed two-parameter problem. Appl. Num. Math. 56 (2006) 962-980
  10. 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.
  11. Meddahi, S.; Sayas, F.J. BEM-FEM coupling for wave-structure interaction. Scientia. Series A: Math. Sci. 13 (2006) 5-12
  12. Oosterlee, C.W.;Gaspar, F.J. Multigrid methods for the Stokes system. Computing in Science and Engineering 8 (2006) 34-43
  13. Rapún, M.L.; Sayas, F.J. Boundary integral approximation of a heat-diffusion problem in time-harmonic regime. Numer. Algorithms 41 (2006) 127-160
  14. 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.
  15. Salazar, A.; Garrido, F.; Celorrio, R.: Thermal diffusivity of rods tubes and spheres by the flash method. J. Appl. Phys. 99 (2006) art.
    066116(1-3). 
  16. Salazar, A.; Celorrio, R. Application of the thermal quadrupole method to the propagation of thermal waves in multilayered cylinders. J. Appl. Phys. 100 (2006) art. 113535
2005
  1. Clavero, C; Gracia, J.L. High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems. Appl. Math. Comp 168 (2005) 1109-1117
  2. Clavero, C; Gracia, J.L.; Jorge, J.C. High Order Numerical Methods for One Dimensional Parabolic Singularly Perturbed Problems with Regular Layers. Numer. Methods Partial Differential Equations, 21 (2005) 149-169.
  3. Clavero, C; Gracia, J.L.; O'Riordan, E. A parameter  robust numerical method for a two dimensional reaction-diffusion problem. Math. Comput. 74 (2005) 1743-1758
  4. Garrido, F.; Salazar, A.; Celorrio, R. Effective thermal diffusivity of composites by the flash method. J Phys IV 125 (2005) 515-517
  5. 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
  6. 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.
  7. Naumovich A., Iliev O., Gaspar F.J., Lisbona F.J., Vabishchevich, P.N, On numerical solution of 1-D poroelasticity equations in a multilayered domain. Math. Model. Anal. 10 (2005) 287-304
  8. Salazar, A.; Garrido, F.; Oleaga, A.; Celorrio, R. Degeneracy of the thermal properties of buried structures. J. Appl. Phys. 98 (2005) art. 013513
2004
  1. Celorrio, R; Dominguez, V.; Sayas, F.J. Overlapped BEM-FEM and some Schwarz iterations. Comput. Methods Appl. Math 4 (2004) no. 1, 3-22
  2. Clavero, C; Gracia, J.L. HODIE finite difference schemes on generalized Shishkin meshes. J. Comput. Appl. Math. 164-165 (2004) 195-206
  3. Gaspar F.J.; Lisbona, F.J.; Oosterlee, C.W.; Wienands, R. A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity problem. Numer. Linear Algebra Appl.11(2004) no.2-3, 93-113.
  4. Gaspar F.J.; Lisbona, F.J.; Oosterlee, C.W.; Wienands, R. An efficient multigrid solver based on distributive smoothing for poroelasticity equations. Computing 73 (2004), no. 2, 99-119.
  5. Gaspar F.J.; Lisbona, F.J.; Vabishchevich,P.N. A Numerical Model for Radial Flow through Porous and Deformable Shells.  Comput. Methods Appl. Math. 4 (2004) no.1, 34-47
  6. Oosterlee, C.W.; Frisch, J.C.; Gaspar, F.J. TVD, WENO and blended BDF discretizations for Asian opions. Comput. Vis. Sci. 6 (2004), no. 2-3, 131--138
  7. Sayas, F.J. Aubin-Nitsche estimates are equivalent to compact embeddings. BIT 44 (2004) no 2., 287-290.
2003
  1. Clavero, C; Lisbona, F.; Jorge, J.C. A Uniformly Convergent Scheme on a Non Uniform Mesh for Convection-Diffusion Parabolic Problems.  J. Comput. Appl. Math. 154 (2003) 415-429.
  2. Domínguez, V. High order quadrature and collocation methods for some logarithmic kernel integral equations. J. Comput. Appl. Math. 161 (2003) 145-159,
  3. Domínguez, V; Sayas, F.-J. An asymptotic series approach to qualocation methods. J. Integral Equations Appl. 15 (2) (2003) 113-151.
  4. Domínguez, V; Sayas, F.J. Stability of discrete liftings. C. R. Math. Acad. Sci. Paris 337 (2003) 805-808.
  5. Gaspar F.J., Lisbona, F.J., Vabishchevich,P.N.  A finite difference analysis of Biot's consolidation model. Appl. Num. Math. 44 (2003) 487-506
  6. Gaspar F.J., Lisbona, F.J., Vabishchevich,P.N.  Finite difference scheme for filtration and consolidation problems. Lecture Notes in Comput. Sci., 2542 (2003) 454-462.
  7. Gracia, J.L;  Jorge, J.C.; Bujanda, B.; Clavero, C.;  High Order Uniformly Convergent Fractional Step RK Methods and HODIE Finite Difference Schemes for 2D Evolutionary Convection-Diffusion Problem. Journal of Computational Methods for Science and Engineering 3 (2003) 403-413
  8. Salazar, A.; Sánchez-Lavega, A.; Celorrio, R. Scattering of cylindrical thermal waves in fiber composites: in-plane thermal diffusivity. J. Appl. Phys. 93, 4536-4542 (2003)
  9. Sayas, F.-J. A nodal coupling of finite and boundary elements. Numer. Methods Partial Differential Equations 19 (2003) 555-570
2002
  1. Celorrio, R.; Domínguez, V.; Sayas, F.J. An interior-exterior Schwarz algorithm and its convervence. C.R.A.S.Paris SerI. Math. 334 (10) (2002) 923-926.
  2. Celorrio, R; Dominguez, V.; Sayas, F.-J. Periodic Dirac delta distributions in the boundary element method. Adv. Comput. Math. 17(3) (2002) 211-236.
  3. Clavero, C.; Gaspar, F.; Lisbona, F. Some numerical experiments with multigrid methods on Shishkin meshes. J. Comput. Appl. Math. 138 (2002) 21-35
  4. Clavero, C; Gracia, J.L.; Lisbona, F.; Shishkin, G.I. A robust method of improved order for convection-diffusion problems in a domain with characteristic boundaries. ZAMM Z. Angew. Math. Mech. 82(9) (2002) 631-647.
  5. Gaspar F.J., Lisbona, F.J., Vabishchevich,P.N. Finite difference schemes for poro-elastic problems.  Comput. Methods Appl. Math. 2 (2002) 132-142.
  6. Salazar, A.; Terrón, J.M; Sánchez-Lavega, A.; Celorrio R. On the effective thermal diffusivity of fiber reinforced composites. Appl. Phys. Let 80(11) (2002) 1903-05.
  7. Sayas, F.J. Asymptotic series in the numerical analysis of boundary element methods (Spanish) Bol. SEMA 20 (2002) 77-96.
2001
  1. Calvo, P.; Lisbona, F. A Finite Volume-Multigrid Method for Flow Simulation on Stratified Porous Media on Curvilinear Coordinate Systems. Int. J. Numer. Meth. Fluids 37 (2001) no.4, 375-397
  2. 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.
  3. Clavero, C.; Miller, J.J.H; O'Riordan, E.; Shishkin, G.I. Numerical experiments for advection-diffusion problems in a chanel with a 180^o bend. J. Comput.Math. 118 (2001), no.2-3, 223-246.
  4. 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
  5. Dominguez, V.; Sayas, F.-J.. Full asymptotics of spline Petrov-Galerkin methods for some periodic pseudodifferential equations. Adv. Comput. Math. 14 (1) (2001) 75-101
  6. Dominguez, V.; Sayas, F.-J.. Local expansions of periodic spline interpolation with some applications. Math. Nach. 227 (2001) 43-62
  7. Gracia, J.L.; Lisbona, F.; Clavero, C. High Order $\varepsilon-$Uniform Methods for Singularly Perturbed Reaction-Diffusion Problems. Lecture Notes in Comput. Sci. 1988 (L. Vulkov, J. Wasniewski, P. Yalamov, eds) (2001), 350-358.
  8. Gaspar, F.; Lisbona, F.; Clavero, C. Multigrid methods and finite difference schemes for 2D singularly perturbed problems. Lecture Notes in Comput. Sci. 1988 (L. Vulkov, J. Wasniewski, P. Yalamov, eds) (2001), 316-324.
  9. Lisbona, F. J.; Vabishchevich, P. N. Operator-splitting schemes for solving unsteady elasticity problems. Comput. Methods Appl. Math. 1 (2001), no. 2, 188--198.
  10. Samarskii, A. A.; Vabishchevich, P. N.; Lisbona, F. Difference schemes for problems of filtration consolidation. (Russian) Dokl. Akad. Nauk 376 (2001), no. 4, 454--457.
2000
  1. Clavero, C.; Jorge, J. C.; Lisbona, F.; Shishkin, G. I. An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems. IMA J. Numer. Anal. 20 (2000), no. 2, 263--280.
  2. 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 
1999
  1. Celorrio, R. Sayas, F.-J. Full collocation methods for some boundary integral equations. Numer. Alogorithms 22 (1999), no. 3-4, 327-351. 
  2. Celorrio, R.; Sayas, F.-J. The Euler-Maclaurin formula in presence of a logarithmic singularity. BIT 39 (1999), no. 4, 780--785.
  3. Clavero, C.; Gracia, J. L.; Lisbona, F. High order methods on Shishkin meshes for singular perturbation problems of convection-diffusion type. Numer. Algorithms 22 (1999), no. 1, 73--97.
  4. 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.
1998
  1. Clavero, C.; Jorge, J. C.; Lisbona, F.; Shishkin, G. I. A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems. Appl. Numer. Math. 27 (1998), no. 3, 211--231. 
  2. Clavero, C.; Miller, J. J. H.; O'Riordan, E.; Shishkin, G. I. An accurate numerical solution of a two-dimensional heat transfer problem with a parabolic boundary layer. J. Comput. Math. 16 (1998), no. 1, 27--39.
  3. Crouzeix, M.; Sayas, F.-J. Asymptotic expansions of the error of spline Galerkin boundary element methods. Numer. Math. 78 (1998), no. 4, 523--547.
  4. Oosterlee, C. W.; Gaspar, F. J.; Washio, T.; Wienands, R. Multigrid line smoothers for higher order upwind discretizations of convection-dominated problems. J. Comput. Phys. 139 (1998), no. 2, 274--307.
  5. Sayas, F.-J. A generalized Euler-Maclaurin formula on triangles. J. Comput.Appl. Math. 93 (1998), no. 2, 89--93.
1997
  1. Aguilar, G.; Lisbona, F. Singular perturbation on a subdomain. J. Math. Anal. Appl. 210 (1997), no. 1, 292--307.
  2. Aguilar, G.; Lisbona, F.; Madaune-Tort, M. Analysis of a nonlinear parabolic-hyperbolic problem. Adv. Math. Sci. Appl. 7 (1997), no.1, 165--181.
  3. Sayas, F.-J. Fully discrete Galerkin methods for systems of boundary integral equations. J. Comput. Appl. Math. 81 (1997), no. 2, 311--331.
1995
  1. Clavero, Carmelo; Lisbona, Francisco; Miller, John J. H. Uniform convergence of arbitrary order on nonuniform meshes for a singularly perturbed boundary value problem. J. Comput. Appl. Math. 59 (1995), no. 2, 155--171.
1994
  1. Aguilar, G.; Lisbona, F. On the coupling of elliptic and hyperbolic nonlinear differential equations. RAIRO Modél. Math. Anal. Numér. 28 (1994), no. 4, 399--418.
  2. Jorge, J. C.; Lisbona, F. Contractivity results for alternating direction schemes in Hilbert spaces. Appl. Numer. Math. 15 (1994), no. 1, 65--75.
1993
  1. Clavero, Carmelo; Lisbona, Francisco Uniformly convergent finite difference methods for singularly perturbed problems with turning points. Numer. Algorithms 4 (1993), no. 4, 339--359.
1990 and 
before
  1. Calvo, M.; Lisbona, F; Montijano, J. On the stability of interpolatory variable-stepsize Adams methods in Nordsieck form. SIAM J. Numer. Anal. 26 (1989), no. 4, 946--962.
  2. Calvo, M.; Lisbona, F.; Montijano, J. On the stability of variable-stepsize Nordsieck BDF methods. SIAM J. Numer. Anal. 24 (1987), no. 4, 844--854.
  3. Crouzeix, M.; Lisbona, F. J. The convergence of variable-stepsize, variable-formula, multistep methods. SIAM J. Numer. Anal. 21 (1984), no. 3, 512--534.
  4. Gasca González, M.; Lisbona, F. J. On the approximation of linear forms. (Spanish) Rev. Mat. Hisp.-Amer. (4) 38 (1978), no. 4-5, 229--241.

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    These pages prepared by Francisco-Javier Sayas
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