Research

Preprints of Recent Work

1. M. R. Correa, G. Taraschi, Primal Hybrid formulations and local stress recovery for Biot problem, (in preparation)

2. G. Taraschi, M. R. Correa, Numerical Analysis of a locking-free primal hybrid method for linear elasticity with H(div)-conforming stress recovery (Submitted, arXiv)

Publications in Journals and Other Works

1. M. R. Correa, M. A. Murad, Fixed-Stress Sequential Schemes for Black-Oil Model in Poroelastic Media, Journal of Computational Physics, vol 543C, pp 114406, (2025). DOI 10.1016/j.jcp.2025.114406 (preprint)

2. G. A. Haveroth, C. J. Thore, R. F. Ausas, S. Jakobsson, J. A. Cuminato, M. R. Correa, Optimization of point-melting strategies for the Electron Beam Melting process, Finite Elements in Analysis and Design, vol 249, pp 104356, (2025). DOI 10.1016/j.finel.2025.104356 (preprint)

3. A. L. A. de Araujo, J. L. Boldrini, B. M. R. Calsavara, M. R. Correa, Analysis and numerical approximation of a mathematical model for Aedes aegypti populations, Computers and Mathematics with Applications, vol 180, pp 214-241, (2025). DOI 10.1016/j.camwa.2025.01.003 (preprint)

4. L. Abdala, C. E. K. Mady, M. R. Correa, A heart chamber model using a capacitance function combined with the Navier-Stokes equations, Mathematical Methods in the Applied Sciences, vol 48, Issue 6, (2025). DOI 10.1002/mma.10682 (preprint)

5. G. A. Haveroth, C. J. Thore, R. F. Ausas, S. Jakobsson, J. A. Cuminato, M. R. Correa, A thermal model for topology optimization in additive manufacturing: design of support structures and geometry orientation, Computers and Structures, vol 301, pp 107453, (2024). DOI 10.1016/j.compstruc.2024.107453 (preprint)

6. E. G. Birgin, M. R. Correa, V. A. Gonzalez-Lopez, J. M. Martinez, D. S. Rodrigues, Randomly supported variation of deterministic models and its application to one-dimensional shallow water flows, Journal of Hydraulic Engineering, vol 150, n.5, pp 04024026, (2024). DOI 10.1061/JHEND8.HYENG-13748 (preprint)

7. M. R. Correa, C. J. Thore, R. F. Ausas, S. Jakobsson, G. A. Haveroth, J. A. Cuminato. A transient thermoelastic mathematical model for topology optimization of support structures in additive manufacturing, Structural and Multidisciplinary Optimization, 67, no. 35, (2024). DOI 10.1007/s00158-024-03757-3

8. G. Taraschi, M. R. Correa, A. S. Pinto, C. O. Faria, A Global H(div)-conforming finite element post-processing for stress recovery in nearly incompressible elasticity, Applied Mathematics and Computation, 470 (2024), pp 128587. DOI 10.1016/j.amc.2024.128587

9. Camila F.A. Lages, Vitoria Y. Nicoleti, M. R. Correa, and others, Automatic crystal identification for crystallography: a comparison between direct methods and artificial intelligence strategies, bioRxiv (2024), DOI 10.1101/2024.08.22.609235

10. G. A. Haveroth, M. R. Correa, and others, Topology Optimization for the Development of Electric Engines, Mathematics in Industry Reports (MIIR) (2023). DOI 10.33774/miir-2023-r48jb

11. M. R. Correa, G. Taraschi, Optimal H(div) flux approximations from the Primal Hybrid Finite Element Method on Quadrilateral Meshes, Computer Methods in Applied Mechanics and Engineering, 400 (2022), pp 115539. DOI 10.1016/j.cma.2022.115539

12. G. Taraschi, M. R. Correa, On the Convergence of the Primal Hybrid Finite Element Methods on Quadrilateral Meshes, Applied Numerical Mathematics, 181, (2022), pp 552-560. DOI 10.1016/j.apnum.2022.07.005

13. G. A. Haveroth, C. J. Thore, M. R. Correa, R. F. Ausas, S. Jakobsson, J. A. Cuminato, A. Klarbing, Topology optimization including a model of the layer-by-layer additive manufacturing process, Computer Methods in Applied Mechanics and Engineering, 398 (2022), pp 115203. DOI 10.1016/j.cma.2022.115203 (preprint)

14. M. A. Murad, M. R. Correa, M. R. Borges, J. A. L. Obreg�n, T. V. Lopes, A Fixed-Stress Split Strategy for Two-Phase Flow in Heterogeneous Poroelastic Media Overlain by Viscoelastic Rock Salt Layers. Computer Methods in Applied Mechanics and Engineering, 380 (2021), pp 113768. DOI 10.1016/j.cma.2021.113768

15. M. R. Correa, J. C. Rodriguez, A. Farias, D. De Siqueira, P. R. B. Devloo, Hierarchical high order finite element spaces in H(div)xH1 for a stabilized mixed  formulation of Darcy problem. Computers and Mathematics with Applications, 80 (2020), pp 1117�1141. DOI 10.1016/j.camwa.2020.06.003

16. T. O. Quinelato, A. F. D. Loula, M. R. Correa, T. Arbogast, Full H(div)-Approximation of Linear Elasticity on Quadrilateral Meshes based on ABF Finite Elements. Computer Methods in Applied Mechanics and Engineering, 347 (2019), pp 120�142. DOI 10.1016/j.cma.2018.12.013

17. M. R. Correa, M. A. Murad, A new sequential method for three-phase immiscible flow in poroelastic media. Journal of Computational Physics, 373 (2018), pp 493�532. DOI 10.1016/j.jcp.2018.06.069

18. A. M. Rocha, J. S. Azevedo, S. P. Oliveira, M. R. Correa, Numerical analysis of a collocation method for functional integral equations. Applied Numerical Mathematics, 134 (2018), pp 31�45. DOI 10.1016/j.apnum.2018.07.002

19. M. R. Correa. A Semi-Discrete Central Scheme for Incompressible Multiphase Flow in Porous Media in Several Space Dimensions. Mathematics and Computers in Simulation, 140 (2017), pp 24�52. DOI 10.1016/j.matcom.2017.01.008

20. T. Arbogast and M. R. Correa, Two Families of H(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension. SIAM Journal on Numerical Analysis (SINUM), 54:6 (2016), pp 3332�3356. DOI 10.1137/15M1013705

21. M. R. Correa and M. R. Borges, A Semi-Discrete Central Scheme for Scalar Hyperbolic Conservation Laws with Heterogeneous Storage Coefficient and its Application to Porous Media Flow. International Journal for Numerical Methods in Fluids, 73 (2013), pp 205--224. DOI 10.1002/fld.3794

22. M. A. Murad, J. A. L. Obreg�n, M. R. Borges, and M. R. Correa, A New Locally Conservative Numerical Method for Two-Phase Flow in Heterogeneous Poroelastic Media. Computers and Geotechnics, 48 (2013), pp. 192--217. DOI 10.1016/j.compgeo.2012.06.010

23. M. A Murad, J. A. L. Obreg�n, T. Lopes, C. Radke, M. R. Correa, M. R. Borges and S. A. de Lima, New Locally Conservative Numerical Schemes for Hydrogeomechanical Couplings in Strongly Heterogeneous Presalt Reservoirs. SPE Reservoir Simulation Symposium, (2013). DOI 10.2118/163601-ms

24. M. R. Correa and A. F. D. Loula, A Unified Mixed Formulation Naturally Coupling Stokes and Darcy Flows. Computer Methods in Applied Mechanics and Engineering, 198 (2009), pp 2710�2722. DOI 10.1016/j.cma.2009.03.016

25. A. F. D. Loula, M. R. Correa, J. N. C. Guerreiro and E. M. Toledo, On Finite Element Methods for Heterogeneous Elliptic Problems. International Journal of Solids and Structures, 45:1 (2008), pp 6436�6450. DOI 10.1016/j.ijsolstr.2008.08.005 (preprint)

26. M. R. Correa and A. F. D. Loula, Unconditionally Stable Mixed Finite Element Methods for Darcy Flow. Computer Methods in Applied Mechanics and Engineering, 197 (2008), pp 1525�1540. DOI 10.1016/j.cma.2007.11.025 (preprint)

27. M. R. Correa and A. F. D. Loula, Stabilized Velocity Post-Processings for Darcy flow in heterogenous porous media. Communications in Numerical Methods in Engineering, 23 (2007), pp 461�489. DOI 10.1002/cnm.904 (preprint)

28. M. R. Correa, A. F. D. Loula and E. L. M. Garcia, M�todos de Diferen�as Finitas de Dire��es Alternadas Impl�citos para Modelagem de �guas Subterr�neas. TEMA - Tend�ncias em Matem�tica Aplicada e Computacional, 5 (2004), pp 65�76. DOI 10.5540/tema.2004.05.01.0065

Dissertations (Advisor/Co-Advisor)

1. D.Sc. Giovanni Taraschi, �M�todos H�bridos Primais com recupera��o de tens�o para problemas quase incompress�veis em elasticidade linear e poroelasticidade� (2025)

2. M.Sc. Breno Ceconello, �Estudo de Formula��es de Elementos Finitos H1-Conformes para Problemas de Poisson em Grafos� (2025)

3. M. Sc. Thiago Felipe Castro Carrenho, ``M�todos Num�ricos para o Sistema de �guas Rasas acoplado � Equa��o de Exner�� (2024)

4. M. Sc. Robson Carlos de Moura Junior, ``Resolu��o Num�rica das Equa��es de Saint-Venant pelo M�todo de Galerkin Descont�nuo�� (2022)

5. M. Sc. Victor Hugo Caldeira Jorge Fialho, ``Modelagem matem�tica e Computacional do Desenvolvimento de Biomassa e Redu��o do Fluxo Hidr�ulico em Meios Porosos Saturados�� (2021)

6. M.Sc. Giovanni Taraschi, ``An�lise Num�rica do M�todo de Elementos Finitos H�brido Primal com Recupera��o de Fluxos Aplicado a um Problema El�ptico de Segunda Ordem'' (2021)

7. D.Sc. Felipe Augusto Guedes da Silva, ``M�todos de Galerkin Descont�nuo de Mais Alta Ordem para Leis de Conserva��o Hiperb�licas'' (2019)

8. M.Sc. Laryssa Abdala (co), ``Heart chamber modeling using Navier-Stokes equations'' (2018)

9. D.Sc. Benedito Silva Abreu, ``Um M�todo de Elementos Finitos Baseado em Fluxos em H(div)'' (2018)

10. M.Sc. Jos� Maria Naranjo Martinez, ``Um Modelo Computacional para o Estudo da Propaga��o da Dengue'' (2017)

11. D.Sc. Juan Carlos Rodriguez Miranda, ``Espa�os hier�rquicos para uma formula��o de elementos finitos mista estabilizada do problema de Darcy'' (2017)

12. D.Sc. Adson Mota Rocha (co), ``An�lise e Aproxima��o de uma Classe de Equa��es Integrais de Fredholm N�o-Lineares'' (2017)

13. D.Sc. Thiago de Oliveira Quinelato (co), ``Mixed Hybrid Finite Element Methods in Elasticity and Poroelasticity'' (2017)

14. D.Sc. Margui Angelica Romero Pinedo, ``M�todos de elementos finitos mistos-h�bridos para um problema el�ptico n�o linear em malhas quadrilaterais'' (2016)

15. M.Sc. Felipe Augusto Guedes da Silva, ``Um estudo de M�todos de Galerkin Descont�nuo de alta ordem para problemas hiperb�licos'' (2015)

16. M.Sc. Thiago de Oliveira Quinelato, ``Formula��es de Elementos Finitos para Problemas Parab�licos Lineares'' (2013)

17. M.Sc. Denise Schimitz de Carvalho Trist�o, ``Esquemas Centrais para Leis de Conserva��o em Meios Porosos'' (2013)

18. M.Sc. Gustavo Miranda Teixeira (co), ``M�todos num�ricos para a solu��o de escoamentos bif�sicos de fluidos incompress�veis em meios porosos'' (2011)