Publications by Sonia M. Gomes

Doctoral Dissertation

Articles in Journals

Articles in Proceedings

Book chapters

Edited books

Lecture Notes

Doctoral Dissertation

S. M. Gomes. Existência e comportamento na fronteira de solução de problema de Dirichlet com singularidade na fronteira.
Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1982. 48 p. 

Articles in Journals

  1. D. Siqueira, S. M. Gomes, P. R. B. Devloo . A new procedure for the construction of hierarchical high order Hdiv and Hcurl finite element spaces. Journal of Computational and Applied Mathematics, v. 240, p. 204-214, 2013.

  2. M O Domingues; A K F Gomes, S. M. Gomes; O M. Mendes Jr. ; B. Pierro; K. Schneider. Extended generalized Lagrangian multipliers for magnetohydrodynamics using adaptive multiresolution methods. ESAIM. Proceedings, v. 43, p. 95-107, 2013.

  3. P. R. B. Devloo, A M. Farias, S. M. Gomes, Sônia M. ; J. L. Gonçalves Application of a combined continuous-discontinuous Galerkin finite element method for the solution of the Girkmann problem. Computers & Mathematics with Applications v. 65, p. 1786-1794, 2013.

  4. Gonçalves, J. L. ; S. M Gomes; P. R. B Devloo. A goal-oriented hp -adaptive discontinuous Galerkin approach for biharmonic problems. International Journal for Numerical Methods in Engineering

  5. D. A Castro.Gomes, Sônia M. ; Stolfi, Jorge . An adaptive multiresolution method on dyadic grids: Application to transport equations. Journal of Computational and Applied Mathematics, v. 236, p. 3636-3646, 2012.

  6. M. Domingues, Gomes, Sônia M. ; Roussel, Olivier ; Schneider, Kai . Adaptive multiresolution methods. ESAIM. Proceedings, v. 34, p. 1-96, 2011.

  7. M. Domingues, P. J. Ferreira, S. M. Gomes, A Gomide J. R. Pereira. P. Pinho. Grid Structure Impact in Sparse Point Representation of Derivatives. Journal of Computational and Applied Mathematics, v. 234, p. 2377-2389, 2010.

  8. R. Deiterding, M. Domingues, S. M. Gomes, O Roussel, K Schneider. Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations. ESAIM. Proceedings, v. 29, p. 28-42, 2009.

  9. M. Domingues, S. M. Gomes, O Roussel, K Schneider. Space time adaptive multiresolution methods for hyperbolic conservation laws: Applications to compressible Euler equations. Applied Numerical Mathematics, v. 59, p. 2303-2321, 2009.

  10. M. Domingues, S. M. Gomes, O Roussel, K Schneider. . An adaptive multiresolution scheme with local time stepping for evolutionary PDEs. Journal of Computational Physics, v. 227, p. 3758-3780, 2008.

  11. P. Pinho, M. O. Domingues, P. J. S. G. Ferreira, S. M. Gomes, A. Gomide e J. R. Pereira.  Interpolating wavelets and adaptive finite difference schemes for solving Maxwell's equations: the effect of gridding. IEEE Transactions on Magnetics 43 (3): 1013 -1022, 2007.

  12. P. R. B. Devloo, P. D. Fernandes, S. M. Gomes, C. M. A. Bravo, R. G. Damas. A finite element model for three dimensional hydraulic fracturing.  Mathematics and Computers in Simulation 73 (1-4): 142 - 155, 2006

  13. J. L. D. Calle, P. R. B. Devloo and S. M. Gomes. Stabilized discontinuous Galerkin method for hyperbolic equations. Computer Methods in Applied Mechanichs and Engineering 194(7):1861-187, 2005

  14. J. L. D. Calle, P. R. B. Devloo and S. M. Gomes. Wavelets and Adaptive Grids for the discontiuous Galerkin method. Numerical Algorithms, 39(1-3): 143-158, 2005.

  15. J. E. Castilho, M. O. Domingues and S. M. Gomes. Multiscale discretization of nonlinear differential operators: pseudo-wavelet
    schemes. Far East Journal of Mathematical Sciences 17: 139-177, 2004

  16. M. O. Domingues, S. M. Gomes and L. M. Alvarez Diaz. Adaptive wavelet representation and differentiation on block-structured grids.Applied Numerical Mathematics, 8(3-4): 421-437, 2003.

  17. S. M. Gomes, A. K. Kushpel, and J. Levesley. Approximation in L2 Sobolev spaces on the 2-sphere by quasi-interpolation. Journal of Fourier Analysis and Applications 7(3): 283-295, 2001.

  18. S. M. Gomes, A. K. Kushpel, J. Levesley and D. L. Ragozin. Interpolation on the torus using sk-splines with number theoretic knots. Journal of Approximation Theory, 98(1): 56 -- 71, 1999.

  19. S. M. Gomes and C. Cunha. The relation between Petrov-Galerkin and collocation methods using spline multiresolution analyses. Revista de la Unión Matemática Argentina, 41(1): 61--78, 1998.

  20. C. Cunha and S. M. Gomes. A schock indicator for adaptive schemes for conservation laws. Journal of Scientific Computing, 12 (2): 205 --214, 1997.

  21. S. M. Gomes and E. Cortina. Convergence estimates for the wavelet-Galerkin method. SIAM Journal on Numerical Analysis , 33(1):149 -- 161, 1996.

  22. S. M. Gomes and C. A. Moura.  Foreword to the special issue on wavelets - theory and applications. Matemática Aplicada e Computacional 15(2): 97-98, 1996.

  23. S. M. Gomes. Convergence estimates for the wavelet-Galerkin method: superconvergence at the node points. Advances in Computational Mathematics , 4: 261--282, 1995.

  24. S. M. Gomes and E. Cortina. Some results on the convergence of sampling series based on convolution integrals. SIAM Journal on Mathematical Analysis , 26 (5): 1386--1402, 1995.

  25. S. M. Gomes and J. Sprekels. Krasnoselskii's theorem on operators compressing a cone: application to some singular boundary value problem. Journal of Mathematical Analysis and Applications . 153(2): 443--459, 1990.

  26. C. J. van Duijn, S. M. Gomes and S. Hongei. On a class of similarity solutions of the equation u_t = (|u|^{m-1} u_x)_x with m > - 1. IMA Journal of Applied Mathematics , 41: 147--163, 1988.

  27. S. M. Gomes. A nonlinear boundary value problem and applications to a diffusion problem with radial symmetries. Matemática Aplicada e Computacional , 6 (2): 141--160, 1987.

  28. S. M. Gomes. On a singular nonlinear elliptic problem}.
    SIAM Journal on Mathematical Analysis . 17(6): 1359--1369, 1986.

  29. S. M. Gomes. Estudio del flujo total en el infinito en un problema de difusión con simetrias radiales. Revista de la Unión Matemática Argentina , 32(2): 134, 1985.

  30. J. E. Bouillet and S. M. Gomes. An equation with a singular nonlinearity related to diffusion problems in one dimension. Quartely of Applied Mathematics , XLII(4): 395--402, 1985.

  31. S. M. Gomes. Desigualdades para la función de Green de operadores elípticos dados en la forma de divergencia. Revista de la Unión Matemática Argentina , 30(1) e (2): 59--60, 1984.

Book Chapters

  1. D. Siqueira ; P. R. B. Devloo; S. M. Gomes. . Coupling Hdiv an H1 Finite Element Approximations for a Poisson Problem. In: Cangiani, A.; Davidchack, R.L.; Georgoulis, E.; Gorban, A.N.; Levesley, J.; Tretyakov, M.V. (Org.). Numerical Mathematics and Advanced Applications 2011. 854ed.Berlin: Springer, 2013, v. , p. 411-418.

  2. M. O Doingues; S. M. Gomes; O Roussel ; K. Schneider,. Space-Time Adaptive Multiresolution Techniques for Compressible Euler Equations. In: de Moura, Carlos A.; Kubrusly, Carlos S. (Org.). The Courant Friedrichs Lewy (CFL) Condition. 01ed.Bassel: Birkhausser, 2013, v. , p. 101-117.

  3. D. Siqueira ; P. R. B. Devloo; Gomes, Sônia M.. . Hierarchical High Order Finite Element Approximation Spaces for H(div) and H(curl). In: Gunilla Kreiss, Per Lötstedt, Axel M lqvist and Maya Neytcheva. (Org.). Numerical Mathematics and Advanced Applications 2009. Berlin: , 2010, v. , p. 269-276.

  4. J. L. Gonçalves; P. R. B. Devloo; S. M. Gomes. Goal-Oriented Error Estimation for the Discontinuous Galerkin Method Applied to the Biharmonic Equation. In: Gunilla Kreiss, Per Lötstedt, Axel M lqvist and Maya Neytcheva. (Org.). Numerical Mathematics and Advanced Applications 2009. Berlin: , 2010, v. , p. 369-376.

  5. H. Bockhorn ; J. A DenevDENEV, J. A. ;M. O Doingues ; C. Falconi; M. Farge ; J. Frohlich ; S. M. Gomes; B. Kadoch ; I. Molina ; ROUSSEL, O. ; SCHNEIDER, K . Numerical Simulation of Turbulent Flows in Complex Geometries Using the Coherent Vortex Simulation Approach Based on Orthonormal Wavelet Decomposition. In: C. Brun; D. Juve; M; Manhart; C-D. Munz. (Org.). Numerical Simulation of Turbulent Flows and Noise Generation. Berlin: , 2009, v. , p. 175-200.

  6. M. K. Kaibara and S. M. Gomes. A fully adaptive multiresolution scheme for shock computations. In: Gudnov Methods: Theory and Applications, p. 497-503, E. F. Toro(ed.) Kluwer Academic/Plenum Publishers, 2001.

  7. M. K. Kaibara and S. M. Gomes. Esquema de Multiresolução adaptativo para leis de conservação. In: Tendências em Matemática Aplicada e Computacional, V. 1.2. E. X. L. de Andrade et al (eds): 389-400. SBMAC, 2000.

  8. J. E. Castilho and S. M. Gomes. Discretization of nonlinear terms using biorthogonal wavelets: hybrid formulations
    In: Approximation Theory IX, vol. II, p. 9-16. C. K. Chui and L. L. Schumaker (eds.). Vanderbilt Univesity Press, 1998.

  9. S. M. Gomes and E. Cortina. Fourier Analysis of the convergence of Petrov-Galerkin methods based on biortogonal wavelets.
    In: Wavelet Theory and Harmonic Analysis in Applied Sciences,p. 119-137. C. E. D'Atellis E. M. F. Berdaguer (eds.). Birkhauser, 1997.

  10. S. M. Gomes, A. K. Kushpel, J. Levesley, and D. L. Ragozin. Sk-spline interpolation on the torus using number theoretic knots.
    In: Curves and Surfaces with Applications in CAGD, p. 143 -- 149. A. Le Méhauté, C. Rabut, and L. L. Schumaker (eds.). Vanderbilt University Press, 1997.

  11. S. M. Gomes, E. Cortina and I. Moroz. Characterization of biorthogonal spline wavelets by means of derivatives and primitives.
    In: Approximation Theory VIII: Wavelets and Multilevel Approximation, vol. II, p. 125-132. C. K. Chui e L. L. Schumaker (eds.). World Scientific Publishing Co., Inc., 1995

  12. E. Cortina and S. M. Gomes. Wavelet method for the Stefan Problem
    In: Fifth Annual Conference of the European Consortium for Mathematics in Industry, p. 197--200, M. Heilio (ed.). B.G. Teubner Stuttgart and Klewer Academic Publishers,1991.

  13. S. M. Gomes. Diffusion controlled growth of precipitate particles: similarity solutions with radial symmetries In: Free boundary problems: theory and applications, Vol. II, p. 861--865. Pitman Res. Notes Math. Ser., 186, Longman Sci. Tech. Harlow, 1990. 

Proceedings

  1. LARSSON, E. ; GOMES, S. M. ; SAFDARI-VAIGHANI, A. ; HERYUDONO, A. . Radial basis function methods in computational finance. In: 13th International Conference Computational and Mathematical Methods in Science and Engineering, 2013, Salamanca. Proceedings CMMSE 2013, 2013.

  2. DEVLOO, P. R. B. ; SANTOS, E. S. R. ; CECILIO, D. L. ; SHAUER, N. ; GOMES, S. M. . Simulação numérica de estabilidade de poços. In: XXXIV CILAMCE, 2013, Pirinópolis. Proceedings do CILAMCE, 2013.

  3. FARIAS, A. M. ; DEVLOO, P. R. B. ; GOMES, S. M. . Simulação multifísica para problemas de acoplamento fluido-estrutura. In: XXXIV CILAMCE, 2013, Pirinópolis. Proceedings do CILAMCE, 2013.

  4. SHAUER, N. ; DEVLOO, P. R. B. ; LUCCI, C. ; FARIAS, A. M. ; GOMES, S. M. . Aproximação numérica elastoplástica de propagação de fraturas hidráulicas bidimensionais. In: XXXIV CILAMCE, 2013, Pirinópolis. Proceedings do CILAMCE, 2013.

  5. DEVLOO, P. R. B. ; CALLE, J. L. D. ; FARIAS, A. M. ; GOMES, S. M. ; LUCCI, C. . Um modelo numérico para a simulação de injeção de vapor em reservatórios. In: CILAMCE 2011, 2011, Ouro Preto. Proceedings do CILANCE, 2011.

  6. DEVLOO, P. R. B. ; FARIAS, A. M. ; GOMES, S. M. ; GONCALVES, J. L. . Semelhança entre o método da dupla projeção Bubnov-Galerkin e o Método de Petrov Galerkin. In: CILAMCE 2011, 2011, Ouro Preto. Proceedings do CILANCE, 2011.

  7. FORTI, T. L. ; DEVLOO, P. R. B. ; GOMES, S. M. . O impacto do uso de funções de enriquecimento no método de Galerkin descontínuo. In: XXX CILANCE, 2009, Armação de Búzios. Proceedings do CILANCE, 2009.

  8. GONCALVES, J. L. ; DEVLOO, P. R. B. ; MOZOLEVSKI, I. ; GOMES, S. M. . Estimativas de erro em quantidades de interesse para soluções obtidas pelo método de Galerkin descontínuo. In: CNMAC, 2008, Belém. Anais do CNMAC, 2008.

  9. FARIAS, A. M. ; GOMES, S. M. ; DEVLOO, P. R. B. . Estimativa a posteriori do erro em termos de quantidades de interesse. In: XXIX CILANCE, 2008, Maceió. XXIX CILANCE, 2008.

  10. FORTI, T. L. ; DEVLOO, P. R. B. ; GOMES, S. M. . Emprego de funções de base singulares em malhas de Galerkin descontínuo. In: XXIX CILANCE, 2008, Maceió. XXIX CILANCE, 2008.

  11. PINHO, P. ; DOMINGUES, M. O. ; FERREIRA, P. J. ; GOMES, S. M. ; GOMIDE, A. ; PEREIRA, J. R. . Adaptive Finite Difference Schemes Based on Interpolating Wavelets for Solving 2D Maxwell´s Equations. In: IEEE AP-S International Symposium on Antennas and Propagation, 2007, Honolulu, Havai. 2007 IEEE AP-S International Symposium on Antennas and Propagation, 2007.

  12. PINHO, P. ; DOMINGUES, M. O. ; FERREIRA, P. J. ; GOMES, S. M. ; GOMIDE, A. ; PEREIRA, J. R. . Resolução das Equações de Maxwell Usando Wavelets Interpolatórias e Esquemas Adaptativos. In: Encontros Ibéricos de Eletromagnetismo Computacional, 2007, Barcelona. Encontros Ibéricos de Eletromagnetismo Computacional, 2007.

  13. PINHO, P. ; GOMES, S. M. ; FERREIRA, P. J. ; PEREIRA, J. R. . Adaptive Method in Space for the Resolution of Maxwell´s Equations. In: 13th International Conference on Telecomunications, 2006, Funchal, Madeira. 13th International Conference on Telecomunications, 2006.

  14. PINHO, P. ; GOMES, S. M. ; FERREIRA, P. J. ; PEREIRA, J. R. ; DOMINGUES, M. O. ; GOMIDE, A. . Resolution of Maxwell´s Equations in a Non Staggered Grid Model. In: First European Conference in Antennas and Propagation, 2006, Nice, França. First European Conference in Antennas and Propagation, 2006.

  15. FERREIRA, P. J. ; GOMES, S. M. ; PEREIRA, J. R. ; PINHO, P. . Análise comparativa de dispersão numérica e estabilidade em diferentes esquemas de diferenças. In: IV Encontro de Electromagnetismo Computacional, 2005, Seia, Portugal. IV Encontro de Electromagnetismo Computacional, 2005.

  16. PINHO, P. ; FERREIRA, P. J. ; GOMES, S. M. ; PEREIRA, J. R. . Solving Maxwell´s equations using interpolating wavelets. In: 5th Conference on Telecomunications, 2005, Lisboa. 5th Conference on Telecomunications.

  17. FORTI, T. L. ; DEVLOO, P. R. B. ; GOMES, S. M. . Método de elementos finitos contínuo e descontínuo combinados aplicado a problemas de convecção-difusão. In: Congresso Ibero Latino Americano de Métodos Computacionais, 2005, Guaraparí. CILANCE2005.

  18. GOMES, S. M. ; KUSHPEL, A. ; LEVESLEY, A. . Approximation In L2 Sobolev Spaces on S2 by Quasi-Interpolation. In: 48 SEMINARIO BRASILEIRO DE ANALISE, 1998, Petrópolis, RJ. -, 1998. p. 643-659.

  19. S. M. Gomes. Unified overview of wavelet-based methods for differential equations (Invited Paper).
    Wavelets and Applications IV , p. 730 -- 739. H. Szu ed. SPIE's AeroSense'97. Orlando, 1997.

  20. E. Cortina and S. M. Gomes. A Petrov-Galerkin method based on biortogonal wavelets for dispersive equations.
    Proceedings do ICIAM 95: Zetschult fur Angewandte Mathematik und Mechanik vol. 1(1) S. 1: 298 -- 315. Alemanha, 1996.

  21. S. M. Gomes and C. Cunha. Shock capturing using interpolatory wavelets.
    Proceedings IEEE MWSCS vol. 2 p. 1119--1121, 1995. L. P. Caloba et al (eds).

  22. S. M. Gomes. M. O. Domingues and E. Cortina. Biorthogonal wavelets applied to METEOSAT image compressing.
    Wavelets and Applications II, p. 726-733, 1995 H. H. Szu (ed.), Proceedings SPIE 2491, 1995 .

  23. C. Cunha and S. M. Gomes. A high resolution numerical method for conservation laws using biorthogonal wavelets.
    XV Congresso Ibero Latino Americano sobre Métodos Computacionais para Engenharias, p. 234-243. Belo Horizonte, 1994.

  24. M. O. Domingues, S. M. Gomes and O. Mendes Jr. Aplicação da transformada wavelet multidimensional no tratamento de imagens METEOSAT. II Congresso Latino-Americano e Ibérico de Meteorologia, p. 449-451 Belo Horizonte, 1994.

  25. L. D. A. Sá, A. Nowosad, A. Druilhet, J-L Atti\'e, P. Duran and S. M. Gomes. Um estudo sobre a aplicação da transformada em ondeletas à análise do sinal turbulento.
    II Congresso Latino-Americano e Ibérico de Meteorologia, p. 5-8 Belo Horizonte, 1994.

  26. P. R. B. Devloo and S. M. Gomes. Finite element algorithms for hyperbolic conservation laws with forcing terms: application to the numerical simulation of hydrazine micro-thrusters.
    Second World Congress on Computational Mechanics, p. 837--841. Stuttgart, Germany 1990.

  27. S. M. Gomes. On similarity solutions for a free boundary problem related to the growth of precipitate particles by diffusion.
    Segundas Jornadas Latino-Americanas de Matemática Aplicada, Rio de Janeiro, 1983. Vol. II p. 935--947.

Edited Books

Seleta do XXII CNMAC - V2 - In cooperation with J. M. Balthazar and A. S. Ranga. SBMAC,
São José do Rio Preto,  2000. 266 p

Seleta do XXII CNMAC - In cooperation with E. X. L. AndradeJ. M. Balthazar, A. S. Ranga and G. N. Silva. SBMAC,
São José do Rio Preto,  2001. 258 p

Seleta do XXIV CNMAC - Parte 1 - In cooperation with E. X. L. Andrade, J. M. Balthazar, A. S. Ranga and G. N. Silva. SBMAC,
São José do Rio Preto,  2002. 239 p

Seleta do XXIV CNMAC - Parte 2 - In cooperation with E. X. L. Andrade, J. M. Balthazar, A. S. Ranga and G. N. Silva. SBMAC,
São José do Rio Preto,  2002. 243 p

Lecture Notes

M. K. Kaibara, S. M. Gomes and M. O. Domingues. Detecção de Singularidades e Compressão de Dados Usando Análise de Multirresolução.  SBMAC, XXIV Congresso Nacional de Matemática Aplicada e Computacional, Belo Horizonte. Setembro, 2001. 44 p. (ps file)

S. M. Gomes, M. O. Domingues and M. K. Kaibara. Navegando de Fourrier a Wavelets.
In: Aplicaçõees em Dinâmica e Controle, p. 243-265,  J. M. Balthazar et al. (eds), ABCM/SBMAC, 2001. ( ps file)

S. M. Gomes and E. Cortina. Wavelet transform: a local time-frequency analysis. 40o. Seminário Brasileiro de Análise: 95-142. Rio de Janeiro, 1994.

Preprints

S. M. Gomes and B. Gustafsson. Combining Wavelets with Finte Differences: Consistency Analysis. Technical Report 2002/01, Uppsala University, 2002

M. O. Domingues, S. M. Gomes and L. M. A. Díaz. Adaptive wavelet representation and differenciation on block-structured grids
Technical Report IMECC- 21/02, 2002 ( ps file or pdf file)

J. L. D. Calle, P. R. B. Devloo and S. M. Gomes. Implicit discontinuous galerkin method for hyperbolic equations. Technical Report IMECC-10/02, 2002 (ps file  or pdf file)

J.  E. Castilho  and S. M. Gomes. A Multilevel Wavelet Scheme for Evolution Equations with Time
Adaptivity. Technical Report IMECC-09/02, 2002 (ps file ) (pdf file)

P . R. B. Devloo, P. D. Fernandes, S. M. Gomes, C. M. A. Bravo and R. G. Damas.  Modelagem numérica de fraturamento hidráulido.  Technical report,