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Leopoldo Penna Franca's publications

We list below publications by Leopoldo Penna Franca. We have checked all those entries where the paper is in a journal but there are quite a number of papers in conference proceedings. Some of these are full papers but others are brief summaries of a talk given at the conference. We have included these since they at least indicate the topic lectured on at the conference in question. The papers are given roughly in chronological order, starting with the earliest, but we have made no attempt to order those published, or delivered, in a given year.


  1. T J R Hughes, L P Franca and M Balestra, A New Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accommodating Equal-Order Interpolations, Computer Methods in Applied Mechanics and Engineering 59 (1) (1986), 85-99.

  2. T J R Hughes, L P Franca and M Mallet, A New Finite Element for Computational Fluid Dynamics: I. Symmetric Forms of the Compressible Euler and Navier-Stokes Equations and the Second Law of Thermodynamics, Computer Methods in Applied Mechanics and Engineering 54 (2) (1986), 223-234.

  3. L P Franca, I Harari, T J R Hughes, M Mallet, F Shakib, T E Spelce, F Chalot and T E Tezduyar, A Petrov-Galerkin Finite Element Method for the Compressible Euler and Navier Stokes Equations, in T E Tezduyar and T J R Hughes (eds.), Numerical Methods for Compressible Flows - Finite Difference, Element and Volume Techniques (The American Society of Mechanical Engineers, New York, 1986), 19-43.

  4. T J R Hughes, M Mallet and L P Franca, New Finite Element Methods for the Compressible Euler and Navier-Stokes Equations, in R Glowinki and J-J Lions (eds.), Computing Methods In Applied Sciences And Engineering VII (North-Holland, Amsterdam, 1986), 339-360.

  5. T J R Hughes, M Mallet and L P Franca, Entropy-Stable Finite Element Methods for Compressible Fluids: Application to High Mach Number Flows with Shocks, in K J Bathe, P G Bergan and W Wunderlich (eds.), Finite element methods for nonlinear problems (Springer-Verlag, Berlin, Heidelberg, 1986), 761-773.

  6. L P Franca, I Harari, T J R Hughes, M Mallet, F Shakib, T E Spelce, F Chalot and T E Tezduyar, A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations, in Numerical Methods for Compressible Flows - Finite Difference, Element and Volume Techniques, 1986, Anaheim (1986), 19-43.

  7. T J R Hughes, M Mallet and L P Franca, New finite element methods for compressible Euler and Navier-Stokes equations, in Computing Methods in Applied Sciences and Engineering VII, 1986, Amsterdam (1986), 360-390.

  8. L P Franca, T J R Hughes, and M Mallet, Entropy-stable finite element methods for compressible fluids: application to high mach number flows with shock, in Europe-US Symposium, 1986, Trodheim (1986), 761-773.

  9. A F D Loula, I Miranda, T J R Hughes and L P Franca, A Successful Mixed Formulation for Axisymmetric Shell Analysis Employing Discontinuous Stress Fields of the Same Order as the Displacement Field, in IV Simpósio Brasileiro Sobre Tubulaçoes e Vasos de Pressao (IV SIBRAT), 1986, Salvador-BA 2 (1986), 581-599.

  10. T J R Hughes, L P Franca and M Balestra, Errata: A New Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accommodating Equal-Order Interpolations, Computer Methods in Applied Mechanics and Engineering 62 (1) (1987), 111.

  11. T J R Hughes and L P Franca, A New Finite Element Formulation for Computational Fluid Dynamics: VII. The Stokes Problem with Various Well-Posed Boundary Conditions: Symmetric formulations that converge for all velocity/pressure spaces, Computer Methods in Applied Mechanics and Engineering 65 (1) (1987), 85-96.

  12. A F D Loula, L P Franca, T J R Hughes and I Miranda, Stability, Convergence and Accuracy of a New Finite Element Method for the Circular Arch Problem, Computer Methods in Applied Mechanics and Engineering 63 (3) (1987), 281-303.

  13. A F D Loula, T J R Hughes, L P Franca and I Miranda, Mixed Petrov-Galerkin Methods for the Timoshenko Beam Problem, Computer Methods in Applied Mechanics and Engineering 63 (2) (1987), 133-154.

  14. A F D Loula, T J R Hughes and L P Franca, Petrov-Galerkin Formulations of the Timoshenko Beam Problem, Computer Methods in Applied Mechanics and Engineering 63 (2) (1987), 115-132.

  15. T J R Hughes, L P Franca and M Mallet, A New Finite Element Formulation for Computational Fluid Dynamics: VI. Convergence Analysis of the Generalized SUPG-Formulation for Linear Time-Dependent Multidimensional Advective-Diffusive Systems, Computer Methods in Applied Mechanics and Engineering 63 (1) (1987), 97-112.

  16. T J R Hughes and L P Franca, Some new classes of mixed finite element methods, in Numerical Analysis 170 (1987), 135-156.

  17. T J R Hughes, L P Franca, I Harari and M Mallet, Finite Element Method for High-Speed Flow: Consistent Calculation of Boundary Flux, in Proceedings of the AIAA 25th Aerospace Science Meeting, 1987 (1987).

  18. L P Franca and T J R Hughes, Two Classes of Mixed Finite Element Methods, Computer Methods in Applied Mechanics and Engineering 69 (1) (1988), 89-129.

  19. T J R Hughes and L P Franca, A Mixed Finite Element Formulation for Reissner Mindlin Plate Theory: Uniform Convergence of all Higher-Order Spaces, Computer Methods in Applied Mechanics and Engineering 67 (2) (1988), 223-240.

  20. T J R Hughes and L P Franca, Convergence of Transverse Shear Stresses in the Finite Element Analysis of Plates, Communications in applied numerical methods 4 (2) (1988), 185-187.

  21. L P Franca, T J R Hughes, A F D Loula and I Miranda, A New Family of Stable Elements for Nearly Incompressible Elasticity Based on a Mixed Petrov-Galerkin Finite Element Formulation, Numerische Mathematik 53 (1) (1988), 123-141.

  22. T J R Hughes, L P Franca, G M Hulbert, Z John and F Shakib, The Galerkin/Least-Squares Method for Advective-Diffusive Equations, in T E Tezduyar and T J R Hughes (eds.), Recent developments in computational fluid dynamics (The American Society of Mechanical Engineers, New York, 1988), 75-99.

  23. T J R Hughes and L P Franca, Some New Classes of Mixed Finite Element Methods, in D F Griffiths and G A Watson (eds.), Numerical analysis 1987 (Longman Scientific & Technical, 1988), 135-156.

  24. T J R Hughes, L P Franca, M Mallet, Z John and F Shakib, The Galerkin/Least-squares method for advective-diffusive equations, in Recent Developments in Computational Fluid Dynamics, 1988, Chicago (1988), 75-99.

  25. L P Franca, On Finite Element Formulations for The Stokes Flow Problem, in Proceedings of II Encontro Nacional de Ciencias Termicas, Aguas de Lindóia-SP (1988), 169-171.

  26. L P Franca, E M Toledo, A F D Loula and E L M Garcia, Stress Analysis in Pressure Vessels by Mixed Finite Element Methods Taking into Account Shear Deformation, in Proceedings of the 5th Brazilian Symposium on Piping and Pressure Vessels 2 (1988), 749-760.

  27. L P Franca and R Stenberg, Finite Element Approximation of a New Variational Principle for Compressible and Incompressible Linear Isotropic Elasticity, Applied Mechanics Reviews 42 (11S) (1989), S64-S68.

  28. L P Franca, Analysis and Finite Element Approximation of Compressible and Incompressible Linear Isotropic Elasticity Based upon a Variational Principle, Computer Methods in Applied Mechanics and Engineering 76 (3) (1989), 259-273.

  29. L P Franca, An Algorithm to Compute the Square Root of a 3 × 3 Positive Definite Matrix, Computer and mathematics with applications 18 (5) (1989), 459-466.

  30. L P Franca and E G D Carmo, The Galerkin Gradient Least-Squares Method, Computer Methods in Applied Mechanics and Engineering 74 (1) (1989), 41-54.

  31. T J R Hughes, L P Franca and G M Hulbert, A New Finite Element Formulation for Computational Fluid Dynamics: VIII. The Galerkin/Least-Squares Method for Advective-Diffusive Equations, Computer Methods in Applied Mechanics and Engineering 73 (1989), 173-189.

  32. L P Franca, I Miranda, T J R Hughes and L P Franca, On Mixed Finite Element Methods for Axisymmetric Shell Analysis, Computer Methods in Applied Mechanics and Engineering 72 (2) (1989), 201-231.

  33. T J R Hughes and L P Franca, The Stokes Problem with Various Well-Posed Boundary Conditions: Symmetric Formulations that Convergence for all Velocity/Pressure Spaces, in T J Chung and G R Karr (eds.), Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville (UAH Press, 1989), 1098-1103.

  34. L P Franca, T J R Hughes, A F D Loula and I Miranda, A New Family of Stable Elements for the Stokes Problem Based on a Mixed Galerkin/Least-Squares Finite Element Formulations, in T J Chung and G R Karr (eds.), Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville (UAH Press, 1989), 1067-1074.

  35. A F D Loula, E M Toledo, L P Franca and E L M Garcia, Application of a mixed Galerkin/Least-squares method for axisymmetric shell problems subjected to arbitrary loading, in Proceedings of the 10th International Conference on Structural Mechanics in Reactor Technology, 1989 (1989), 359-364.

  36. L P Franca and E G D Carmo, Strong source heat transfer simulations based on a Galerkin/Gradient-least-squares method, in Sixth International Conference on Numerical Methods in Thermal Problems, 1989, Swansea (1989), 160-169.

  37. T J R Hughes and L P Franca, The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces, in Seventh International Conference on Finite Element Methods in Flow Problems, 1989, Alabama (1989), 1098-1103.

  38. L P Franca, T J R Hughes, A F D Loula and I Miranda, A new family of stable elements for the Stokes problem based on a mixed Galerkin/Least-squares finite element formulation, in Seventh International Conference on Finite Element Methods in Flow Problems, 1989, Huntsville (1989), 1067-1074.

  39. L P Franca and T J R Hughes, Galerkin-Least-Squares Finite Element Formulations For The Stokes Flow Problem, in Proceedings of the Vth International Symposium on Numerical Methods in Engineering 2 (1989), 99-104.

  40. L P Franca, T J R Hughes and R Stenberg, Finite Element Approximations of the Stokes Flow Problem Based upon Various Variational Principles, in Sixth International Conference on Numerical Methods in Laminar & Turbulent Flow, 1989, Swansea (1989), 85-95.

  41. L P Franca, Finite Element Approximation of a New Variational Principle for Compressible and Incompressible Linear Isotropic Elasticity, in Proceedings of the I Pan American Congress of Applied Mechanics (PACAM), 1989 (1989), 313-315.

  42. L P Franca, On the superconvergence of the Satisfying-Babuska-Brezzi method, International Journal for Numerical Methods in Engineering 29 (8) (1990), 1715-1726.

  43. L P Franca and R Stenberg, An optimal linear element for Reissner-Mindlin plates, in Proceedings of the Second World Congress on Computational Mechanics, 1990, Stuttgart, Germany (1990), 429-432.

  44. L P Franca and S L Frey, Galerkin-least-squares and Galerkin-gradient-least-squares: Modern finite element formulations, in Proceedings of the Second World Congress on Computational Mechanics, 1990 (1990), 18-21.

  45. L P Franca, S L Frey, R Sampaio and R Stenberg, Numerical experiments for the Stokes flow employing Galerkin and Galerkin-least-squares finite element methods, in Proceedings of the Second World Congress on Computational Mechanics, 1990 (1990), 248-251.

  46. L P Franca, F J Karam Filho, A F D Loula and R Stenberg, A convergence analysis of a stabilized method for the Stokes Flow, Matemática Aplicada e Computacional 10 (1) (1991), 19-26.

  47. L P Franca and A F D Loula, A new mixed finite element method for the Timoshenko beam problem, Mathematical Modelling And Numerical Analysis 25 (5) (1991), 561-578.

  48. L P Franca and R Stenberg, Error Analysis of Galerkin Least-Squares Methods for the Elasticity Equations, SIAM Journal on Numerical Analysis 28 (6) (1991), 1680-1697.

  49. L P Franca, S L Frey and T J R Hughes, Stabilized finite element methods for the advective-diffusive problem, in Proceedings of the 11th ABCM Mechanical Engineering Conference, 1991, São Paulo-SP (1991), 97-100.

  50. L P Franca, S L Frey and T J R Hughes, On stabilized methods for the advective-diffusive model, in Proceedings of the 10th International Conference on Computing Methods in Applied Sciences and Engineering, 1991 (1991), 609-620.

  51. R Stenberg, T Vihinen and L P Franca, A nonconforming element for the Reissner-Mindlin plate bending model, in Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics 4 (1991), 1907-1908.

  52. L P Franca and R Stenberg, A modification of a low-order Reissner-Mindlin plate bending element, in The Mathematics of Finite Elements and Applications VII, 1991 (1991), 425-436.

  53. L P Franca and S L Frey, Stabilized finite element methods: II. The incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering 99 (2-3) (1992), 209-233.

  54. F Brezzi, M O Bristeau, L P Franca, M Mallet and G Rogé, A relationship between stabilized finite element methods and the Galerkin method with bubble functions, Computer Methods in Applied Mechanics and Engineering 96 (1) (1992), 117-129.

  55. L P Franca, S L Frey and T J R Hughes, Stabilized finite element methods: I. Application to the advective-diffusive model, Computer Methods in Applied Mechanics and Engineering 95 (2) (1992), 253-276.

  56. S L Frey, L P Franca and R Sampaio, Simulaçao numérica do problema de Navier-Stokes incompressível via métodos estabilizados de elementos finitos, in Proceedings of the IV ENCIT, 1992 (1992), 329-332.

  57. S L Frey, L P Franca and R Sampaio, Stabilized methods for the incompressible Navier-Stokes flow, in International Congress on Numerical Methods in Engineering and Applied Sciences, 1992, Concepción (1992), 796-805.

  58. L P Franca and A L Madureira, Element diameter free stability parameters for stabilized methods applied to fluids, Computer Methods in Applied Mechanics and Engineering 105 (3) (1993), 395-403.

  59. L P Franca and T J R Hughes, Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering 105 (2) (1993), 285-298.

  60. C Baiocchi, F Brezzi and L P Franca, Virtual bubbles and the Galerkin-least-squares method, Computer Methods in Applied Mechanics and Engineering 105 (1993), 125-141.

  61. M A Behr, L P Franca and T E Tezduyar, Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows, Computer Methods in Applied Mechanics and Engineering 104 (1) (1993), 31-48.

  62. L P Franca, T J R Hughes and R Stenberg, Stabilized finite element methods for the Stokes problem, in M D Gunzburger and R A Nicolaides (eds.), Incompressible Computational Fluid Dynamics - Trends and Advances 4 (Cambridge University Press, Cambridge, 1993), 87-108.

  63. L P Franca and C Farhat, On the limitations of bubble functions, Computer Methods in Applied Mechanics and Engineering 117 (1-2) (1994), 225-230.

  64. L P Franca and C Farhat, Anti-stabilizing effects of bubble functions, in Proceedings of the Third World Congress on Computational Mechanics 2 (1994), 1452-1453.

  65. L P Franca, S L Frey and A L Madureira, Two- and three-dimensional simulations of the incompressible Navier-Stokes Equations based on stabilized methods, in Proceedings of the Second European Computational Fluid Dynamics Conference 1994 (1994), 121-128.

  66. L P Franca, Incompressible flows based upon stabilized methods, in Numerical Methods for the Navier-Stokes Equations 47 (1994), 89-100.

  67. L P Franca and F Valentin, Combining stabilized finite element methods, Computational and Applied Mathematics 14 (3) (1995), 285-300.

  68. L P Franca and C Farhat, Bubble functions prompt unusual stabilized finite element methods, Computer Methods in Applied Mechanics and Engineering 123 (1) (1995), 229-308.

  69. L P Franca, C Farhat and M Lesoinne, Static condensation: an old idea revisited, in Cuarto Congreso Franco-Latinoamericano de Matemáticas Aplicadas: Métodos Numéricos en Mecánica, 1995, Concepción (1995), 26.

  70. L P Franca and C Farhat, Unusual stabilized finite element methods, in International Congress on Industrial and Applied Mathematics, ICIAM 95, Hamburg (1995).

  71. L P Franca, C Farhat and M Lesoinne, Stabilized finite element methods suggested by the Galerkin method enriched with bubble functions, in Third U.S. National Congress on Computational Mechanics, 1995, Dallas (1995), 91.

  72. M Lesoinne, C Farhat and L P Franca, Unusual stabilized finite element methods for second order linear differential equations, in Proceedings of the Ninth International Conference on Finite Elements in Fluids - New Trends and Applications, 1995 (1995), 377-386.

  73. L P Franca and R Russo, Approximation of the Stokes problem by residual-free macro bubbles, East West Journal Numerical Analysis 4 (4) (1996), 265-278.

  74. F Brezzi, L P Franca, T J R Hughes and A Russo, Some recent results on the stabilization of finite element methods, in Proceedings of the III Congresso Nazionale della SIMAI, 1996 (Salice Terme, 1996), 596-598.

  75. L P Franca and R Russo, Deriving upwinding, mass lumping and selective reduced integration by residual-free bubbles, Applied Mathematics Letters 9 (1996), 83-88.

  76. L P Franca, C Farhat, A P Macedo and M Lesoinne, Residual-free bubbles for the Helmholtz equation, International Journal for Numerical Methods in Engineering 40 (21) (1997), 4003-4009.

  77. F Brezzi, L P Franca, T J R Hughes and A Russo, b = α g, Computer Methods in Applied Mechanics and Engineering 145 (3-4) (1997), 329-339.

  78. L P Franca and R Russo, Unlocking with residual-free bubbles, Computer Methods in Applied Mechanics and Engineering 142 (3-4) (1997), 361-364.

  79. L P Franca and R Russo, Mass lumping emanating from residual-free bubbles, Computer Methods in Applied Mechanics and Engineering 142 (3-4) (1997), 353-360.

  80. F Brezzi, L P Franca, T J R Hughes and A Russo, Stabilization Techniques and Subgrid Scales Capturing, in Proceedings of a conference on the State of the Art in Numerical Analysis, York (1997), 391-406.

  81. L P Franca, An Overview of the Residual-Free-Bubbles Method, in Numerical Methods in Mechanics 371 (1997), 83-92.

  82. L P Franca and A Russo, Residual-free bubbles and the Stokes problem, in Fourth U.S. National Congress on Computational Mechanics, 1997, San Francisco (1997), 85.

  83. L P Franca and A P Macedo, Computations with a Two-Level Finite Element Method, in Fourth U.S. National Congress on Computational Mechanics, 1997, San Francisco (1997), 84.

  84. L P Franca and A P Macedo, A Two-Level Finite Element Method, in American Mathematical Society Memphis, Tennessee Meeting, 1997, Tennessee (1997), 298.

  85. L P Franca, A Nesliturk and M Stynes, On the stability of residual-free bubbles for convection-diffusion problems and their approximation by a two-level finite element method, Computer Methods in Applied Mechanics and Engineering 166 (1) (1998), 35-49.

  86. F Brezzi, L P Franca and R Russo, Further considerations on residual-free bubbles for advective-diffusive equations, Computer Methods in Applied Mechanics and Engineering 166 (1-2) (1998), 25-36.

  87. L P Franca and A P Macedo, A two-level finite element method and its application to the Helmholtz equation, International Journal for Numerical Methods in Engineering 43 (1) (1998), 23-32.

  88. L P Franca, C Farhat, M Lesoinne and A Russo, Unusual stabilized finite element methods and residual-free-bubbles, International Journal for Numerical Methods in Fluids 27 (1-4) (1998), 159-168.

  89. F Brezzi, L P Franca, D Marini and A Russo, Stabilization techniques for domain decomposition methods with non-matching grids, Domain Decomposition Methods in Sciences and Engineering, in Proceedings of the 9th Domain Decomposition Method Conference held at Bergen (Domain Decomposition Press, Bergan, 1998), 1-11.

  90. L P Franca and A Russo, Stabilization for bilinear finite elements via residual-free bubbles, in Fourth World Congress on Computational Mechanics, 1998, Buenos Aires, 1998 (CERIDE, Santa Fe, Argentina, 1998), 129.

  91. L P Franca, Recent advances on stabilization techniques via bubble functions, in Fourth World Congress on Computational Mechanics, 1998, Buenos Aires, 1998 (CERIDE, Santa Fe, Argentina, 1998), 123.

  92. L P Franca and F Valentin, On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation, Computer Methods in Applied Mechanics and Engineering 190 (13) (2000), 1785-1800.

  93. L P Franca and A Russo, Recovering SUPG using Petrov-Galerkin formulations enriched with adjoint residual-free bubbles, Computer Methods in Applied Mechanics and Engineering 182 (3) (2000), 333-339.

  94. I Harari, L P Franca and S P Oliveira, Streamline design of stability coefficients for the standard family of stabilized methods, in ENCIT 2000, 2000, Porto Alegre-RS (2000).

  95. C Farhat, I Harari and L P Franca, A discontinuous finite element method for the Helmholtz equation, in European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona (2000).

  96. L P Franca, Stabilized finite element methods, in M Deville and R Owens (eds.), Proceedings of the16th IMACS World Congress, Lausanne 2000 (2000).

  97. C Farhat, I Harari and L P Franca, Improved finite element computation of time-harmonic acoustics by discontinuous plane-wave enrichment, in Proceedings of the Fourteenth Engineering Mechanics Conference (EM) 2000, Austin, Texas, May 21-24 (2000).

  98. C Farhat, I Harari and L P Franca, The discontinuous enrichment method, Computer Methods in Applied Mechanics and Engineering 190 (48) (2001), 6455-6479.

  99. L P Franca and A Nesliturk, On a two-level finite element method for the incompressible Navier-Stokes equations, International Journal for Numerical Methods in Engineering 52 (4) (2001), 433-453.

  100. I Harari, L P Franca and S P Oliveira, Streamline design of stability parameters for advection-diffusion problems, Journal of Computational Physics 171 (1) (2001), 115-131.

  101. L P Franca and F Valentin, On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation, in 5th U.S. National Congress on Computational Mechanics, 1999, Boulder, 1999, International Journal for Numerical Methods in Engineering 52 (1-2) (2001), 220.

  102. L P Franca and A Nesliturk, Recent advances on two-level finite element methods, in 5th U.S. National Congress on Computational Mechanics, 1999, Boulder, 1999, International Journal for Numerical Methods in Engineering 52 (1-2) (2001), 211.

  103. L P Franca and F N Hwang, Refining the submesh strategy in the two-level finite element method: application to the advection-diffusion equation, International Journal for Numerical Methods in Fluids 39 (2) (2002), 161-187.

  104. I Harari, S L Frey and L P Franca, A note on a recent study of stabilized finite element computations for heat conduction, Computational Mechanics 28 (1) (2002), 63-65.

  105. L P Franca and L Tobiska, Stability of the residual free bubble method for bilinear finite elements on rectangular grids, IMA Journal of Numerical Analysis 22 (1) (2002), 73-87.

  106. L P Franca and S P Oliveira, Pressure bubbles stabilization features in the Stokes problem, Computer Methods in Applied Mechanics and Engineering 192 (16) (2003), 1929-1937.

  107. L Catabriga, A L Coutinho and L P Franca, Evaluating the LCD algorithm for solving linear systems of equations arising from implicit SUPG formulation of compressible flows, International Journal for Numerical Methods in Engineering 60 (9) (2004), 1513-1534.

  108. T J R Hughes, G Scovazzi and L P Franca, Multiscale and Stabilized Methods, in E Stein, R Borst, T J R Hughes (eds.), Encyclopedia of Computational Mechanics (John Wiley & Sons, Ltd, 2004).

  109. L P Franca, G Hauke and A Masud, Stabilized finite element methods, in L P Franca, T E Tezduyar and A Masud (eds.), Finite Element Methods: 1970's and Beyond (CIMNE, Barcelona, Spain, 2004), 127-139.

  110. L P Franca, T E Tezduyar and A Masud, Preface, in L P Franca, T E Tezduyar and A Masud (eds.), Finite Element Methods: 1970's and Beyond (CIMNE, Barcelona, Spain, 2004).

  111. L P Franca and T G Huntley, On residual-free bubble finite element methods for the Helmholtz equation, in G Seriani and D Lee (eds.), Proceedings of the 4th International Conference on Theoretical and Computational Acoustics, 1999 (World Scientific Publishing, 2004).

  112. L P Franca, J V A Ramalho and F Valentin, Multiscale and residual-free bubble functions for reaction-advection-diffusion problems, International Journal for Multiscale Computational Engineering 3 (3) (2005), 297-312.

  113. L P Franca, A L Madureira, L Tobiska and F Valentin, Convergence analysis of a multiscale finite element method for singularly perturbed problems, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 4 (3) (2005), 839-866.

  114. L P Franca, A L Madureira and F Valentin, Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions, Computer Methods in Applied Mechanics and Engineering 194 (27) (2005), 3006-3021.

  115. L P Franca, J V A Ramalho and F Valentin, Enriched finite element methods for unsteady reaction-diffusion problems, Communications in Numerical Methods in Engineering 22 (6) (2006), 619-626.

  116. L P Franca, G Hauke and A Masud, Revisiting stabilized finite element methods for the advective-diffusion equation, Computer Methods in Applied Mechanics and Engineering 195 (13-16) (2006), 1560-1572.

  117. L P Franca, V John, G Matthies and L Tobiska, An inf-sup stable and residual-free bubble element for the Oseen equations, SIAM Journal on Numerical Analysis 45 (6) (2007), 2392-2407.

  118. G R Barrenechea, L P Franca and F Valentin, A Petrov-Galerkin enriched method: A mass conservative finite element method for the Darcy equation, Computer Methods in Applied Mechanics and Engineering 196 (21-24) (2007), 2449-2464.

  119. L P Franca, S P Oliveira and M Sarkis, Continuous Q1-Q1 Stokes elements stabilized with non-conforming null edge average velocity functions, Mathematical Models and Methods in Applied Sciences 19 (17) (2007), 439-459.

  120. J Dolbow and L P Franca, Residual-free bubbles for embedded Dirichlet problems, Computer Methods in Applied Mechanics and Engineering 197 (45-48) (2008), 3751-3759.

  121. A Masud and L P Franca, A hierarchical multiscale framework for problems with multiscale source terms, Computer Methods in Applied Mechanics and Engineering 197 (33-40) (2008), 2692-2700.

  122. G R Barrenechea, L P Franca and F Valentin, A Symmetric Nodal Conservative Finite Element Method for the Darcy Equation, SIAM Journal on Numerical Analysis 47 (5) (2009), 3652.

  123. L P Franca, C Harder and F Valentin, On a residual local projection method for the Darcy equation, Comptes Rendus. Mathématique 347 (17) (2009), 1105-1110.

  124. G R Barrenechea, L P Franca and F Valentin, Stabilization arising from PGEM: A review and further developments, Applied Numerical Mathematics 59 (9) (2009), 2065-2081.

  125. C A A Henao, A L G A Coutinho and L P Franca, A stabilized method for transient transport equations, Computational Mechanics 46 (1) (2010), 99-204.

  126. A L G A Coutinho, L P Franca and F Valentin, Simulating transient phenomena via residual free bubbles, Computer Methods in Applied Mechanics and Engineering 200 (25) (2011), 2127-2130.
    Last Updated November 2022