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RESEARCH AREAS Numerical analysis and computational mathematics: modeling and the development and analysis of numerical methods for partial differential equations (PDEs) and integro-differential equations, and machine learning for PDEs, including theory (convergence, stability analysis) and applications. ORCID ID 0000-0002-2651-5083 Ciência ID 6410-69EA-9882 RESEARCH UNIT Centro de Matemática da Universidade de Coimbra EDITORSHIP Associate editor of the SeMA Journal. PROJECTS Optical Coherence Elastography for imaging retina mechanical properties (FCT Research Project ICDT - SAICT/032162 - ElastoOCT) Efficient Simulation and Computation for Health, Sea and Industry (FCT Research Project POCI-01-0145-FEDER-028118) Numerical Analysis of Nonlinear Nonlocal Evolution Problems (Ministerio de Economía y Competitividad MTM2014-54710-P) additive.MILLING - Add Milling to Additive Manufacturing, (European Regional Development Fund through the Partnership Agreement PT2020, PT2020-POCISII& DT 3414) Reaction
Optical Modelling of the Human Retina in Health and Disease: from structure to function (FCT Research Project PTDC/SAU-ENB/119132/2010) Multiscale mathematical models for bone remodeling with applications in dentistry (L’Oréal Portugal Medals of Honor For Women in Science, 2010) M. Santos; A. Araújo; S. Barbeiro; S. Clain; R. Costa; G. J. Machado, Very High-Order Accurate Discontinuous Galerkin Method for Curved Boundaries with Polygonal Meshes , Journal of Scientific Computing (2024) S. Barbeiro; R. Henriques; J. L. Santos, A quadratic optimization program for the inverse elastography problem , Journal of Mathematics in Industry (2024). S. Barbeiro; R. Enguiça; D. Lobo., Automatic Generation of Conformal Cooling Channels in Injection Moulding , Computer-Aided Design (2022): 103312-103312. S. Barbeiro, D. Lobo, Learning Stable Nonlinear Cross-Diffusion Models for Image Restoration , Journal of Mathematical Imaging and Vision 62 2 (2019): 223-237. S. Barbeiro, Accuracy of a coupled mixed and Galerkin finite element approximation for poroelasticity, Portugaliae Mathematica, 75 (3-4) (2018), pp. 249–265. DOI 10.4171/PM/2018. A. Araújo, S. Barbeiro, M. Khaksar Galati, Convergence of an explicit iterative leap-frog discontinuous Galerkin method for time-domain Maxwell’s equations in anisotropic materials,Journal of Mathematics in Industry, 8:9 (2018). DOI: https://doi.org/10.1186/s13362-018-0051-6. S. Barbeiro, S. Gh. Bardeji, J. A. Ferreira, L. Pinto, Non-Fickian convection-diffusion models in porous media, Numerische Mathematik, 138 (4) (2018), pp. 869–904. DOI: 10.1007/s00211-017- 0922-6 A. Araújo, S. Barbeiro, M. Khaksar Galati, Stability of a leap-frog discontinuous Galerkin method for time-domain Maxwell’s equations in anisotropic materials, Communications in Computational Physics, 21(5) (2017), pp. 1350–1375. DOI: 10.4208/cicp.OA-2016-0110 A. Araújo, S. Barbeiro, E. Cuesta, A. Durán, Cross-diffusion systems for image processing: II. The linear case, Journal of Mathematical Imaging and Vision, 58 (3) (2017), pp. 447–467. DOI:10.1007/ s10851-017-0720-x. A. Araújo, S. Barbeiro, E. Cuesta, A. Durán, Cross-diffusion systems for image processing: I. The linear case, Journal of Mathematical Imaging and Vision, 58 (3) (2017), pp. 447–467. DOI:10.1007/ s10851-017-0720-x. A. Araújo, S. Barbeiro, P. Serranho, Stability of finite difference schemes for nonlinear complex reaction-diffusion processes, IMA Journal of Numerical Analysis, 35 (3) (2015), pp. 1381–1401. DOI: https://doi.org/10.1093/ imanum/dru037 A. Araújo, S. Barbeiro, P. Serranho, Convergence of finite difference schemes for nonlinear complex reaction-diffusion processes, SIAM Journal on Numerical Analysis 53 (1) (2015), pp. 228– 250. DOI:10.1137/130933642 . A. Araújo, S. Barbeiro, P. Serranho, Stability of finite difference schemes for nonlinear complex reaction-diffusion processes, IMA Journal of Numerical Analysis, 2014. DOI: 10.1093/imanum/dru037. S. Barbeiro, S. GH. Bardeji and J. Ferreira, Laplace transform – Finite element method for non Fickian flows, Computer Methods in Applied Mechanics and Engineering, vol. 261-262, pp. 16–23, 2013. A. Araújo, S. Barbeiro and P. Serranho, Stability of finite difference schemes for complex diffusion processes, SIAM J. Numer. Anal., vol. 50, n. 3, pp. 1284-1296, 2012. S. Barbeiro, J.A. Ferreira, L. Pinto, H1-second order convergent estimates for non Fickian models, Applied Numerical Mathematics, 61, 201–215, 2011. Rui Bernardes, Cristina Maduro, Pedro Serranho, Adérito Araújo, Sílvia Barbeiro, José Cunha-Vaz, Improved adaptive complex diffusion despeckling filter, Optics Express, Vol. 18, Issue 23, pp. 24048-24059, 2010. Sílvia Barbeiro, Mary F. Wheeler, A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability, Computational Geosciences, v. 14, n. 4, 755-768, 2010.
S. Barbeiro, J.A. Ferreira, Coupled vehicle-skin models for drug
release, Comput. Methods Appl. Mech. Engrg. 198, 2078-2086, 2009.
S. Barbeiro, Supraconvergent cell-centered scheme for two dimensional elliptic problems, Applied Numerical Mathematics, 59, 56-72, 2009.
S. Barbeiro, Discretely compact imbeddings in spaces of cell-centered grid functions, Numerical Functional analysis and Optimization, 29:5, 491-506, 2008.
S. Barbeiro, J.A. Ferreira, Integro-differential models for percutaneous drug absorption, International Journal of Computer Mathematics, 84, 451-467, 2007.
S. Barbeiro, J.A. Ferreira, R.D. Grigorieff, Supraconvergence of a finite difference scheme for solutions in H^s(0,L), IMA J. Numer. Anal., 25, 797-811, 2005.
S. Barbeiro, J.A. Ferreira, A superconvergent piecewise linear finite element method for elliptic systems of partial differential equations, J. Comput. Appl. Math., 177, 287-300, 2005. S. Barbeiro, J.A. Ferreira, J. Brandts, Superconvergence of piecewise linear semi-discretizations for parabolic problems with non uniform triangulations, J. Math. Fluid Mech., 7, 192-214, 2005.
S. Barbeiro, J.A. Ferreira, A nonstandard linear finite element method for a planar elasticity problem, Applied Numerical Mathematics 37, 331-340, 2001.
S. Barbeiro,Normas Duais Discretas em Problemas Elípticos , Phd Thesis, Universidade de Coimbra, 2005. S. Barbeiro, Supraconvêrgencia em Métodos de Diferenças Finitas Elípticos, Master Thesis, Universidade de Coimbra, 2000. |
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