Publications

Preprints

1. D. Amigo, F. Lepe, E. Otarola, G. Rivera
   A virtual element method for a convective Brinkman-Forchheimer problem coupled with a heat equation.
   Submitted. (pdf)

2. D. Amigo, F. Lepe and N. Verma
   A conforming virtual element method for the Oseen eigenvalue problem.
   Submitted. (pdf)

3. F. Fuica, F. Lepe and P. Venegas
   Error estimates for a bilinear optimal control problem of Maxwell's equations.
   Submitted. (pdf)

4. D. Adak, F. Lepe and G. Rivera
   A nonconforming virtual element approximation for the Oseen eigenvalue problem.
   Submitted. (pdf)

5. A. Khan, F. Lepe and J. Vellojin
   Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media.
   Submitted. (pdf)

6. A. Khan, F. Lepe, D. Mora and J. Vellojin
   Finite element analysis of the nearly incompressible linear elasticity eigenvalue problem with variable coefficients.
   Submitted. (pdf)

7. D. Amigo, F. Lepe and G. Rivera
   A priori and a posteriori error analysis for a VEM discretization of the convection-diffusion eigenvalue problem.
   Submitted. (pdf)

8. F. Lepe, J. Querales, J. Vellojin and P. Venegas
   A posteriori analysis for the three dimensional acoustic problem.
   Submitted. (pdf)

9. D. Adak, F. Lepe and G. Rivera
   VEM approximation for the Stokes eigenvalue problem: a priori and a posteriori error analysis.
   Submitted. (pdf)

Published or Accepted for Publication

1. F. Lepe, G. Rivera and J. Vellojin
   Finite element analysis for the Navier-Lamé eigenvalue problem.
   Applied Numerical Mathematics, (Accepted).

2. F. Lepe, G. Rivera and J. Vellojin
   Finite element analysis of the Oseen eigenvalue problem.
   Computer Methods in Applied Mechanics and Engineering, Vol. 425, Paper No. 116959, 23 pp., (2024).

3. E. Hernández, F. Lepe, and J. Vellojin
   A mixed parameter formulation with applications to linear viscoelastic slender structures.
   ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 58, No 1, pp. 157 - 189, (2024).

4. F. Lepe, D. Mora and J. Vellojin
   Discontinuous Galerkin methods for the acoustic vibration problem.
   Journal of Computational and Applied Mathematics, 441, Paper No. 115700, 21 pp. (2024).

5. F. Lepe and J. Vellojin
   A posteriori analysis for a mixed formulation of the Stokes spectral problem.
   Calcolo, Vol. 60, 4, article 52, 28 pages, (2023).

6. F. Lepe and G. Rivera
   VEM discretization allowing small edges for the reaction-convection-diffusion equation: source and spectral problems.
   ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 57, Number 5, pp. 3139--3164, (2023).

7. D. Amigo, F. Lepe and G. Rivera
   A virtual element method for the elasticity spectral problem allowing for small edges.
   Journal of Scientific Computing, Vol. 97, article No. 54, 29 pp., (2023).

8. F. Lepe
   Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problem.
   Advances in Computational Mathematics, Vol. 49, 4, article No. 60, 31 pp., (2023).

9. D. Amigo, F. Lepe and G. Rivera
   A virtual element method for the elasticity problem allowing small edges.
   Calcolo, Vol. 60, 2, article No. 28, 34 pp., (2023).

10. D. Inzunza, F. Lepe and G. Rivera
    Displacement-Pseudostress formulation for the linear elasticity spectral problem.
    Numerical Methods for Partial Differential Equations, Vol. 39, 3, pp. 1996--2017, (2023).

11. F. Lepe, D. Mora, G. Rivera and I. Velásquez
    A posteriori virtual element method for the acoustic vibration problem.
    Advances in Computational Mathematics, Vol. 49, 1, Paper No. 10, 29 pp., (2023).

12. F. Fuica, F. Lepe, E. Otárola and D. Quero
    An optimal control problem for the stationary Navier--Stokes equations with point sources.
    Journal of Optimization Theory and Applications, Vol. 196, 2, pp. 590--616, (2023).

13. F. Lepe, G. Rivera and J. Vellojin
    Error estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problem.
    Journal of Computational and Applied Mathematics, Vol. 420, Paper No. 114798, 20 pp., (2023).

14. F. Lepe, G. Rivera and J. Vellojin
    A posteriori analysis for a mixed FEM discretization of the linear elasticity spectral problem.
    Journal of Scientific Computing, Vol. 93, 1, 25 pp., (2022).

15. F. Lepe, G. Rivera and J. Vellojin
    Mixed methods for the velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem.
    SIAM Journal on Scientific Computing, Vol. 44, 3, pp. A1358--A1380, (2022).

16. F. Lepe, D. Mora, G. Rivera and I. Velásquez
    A virtual element method for the Steklov eigenvalue problem allowing small edges.
    Journal of Scientific Computing, vol. 88, 2, Paper No. 44, 21 pp., (2021).

17. F. Lepe, E. Otárola, and D. Quero
    Error estimates for FEM discretizations of the Navier-Stokes equations with Dirac measures.
    Journal of Scientific Computing, Vol. 87, (2), pp. 23, (2021).

18. F. Fuica, F. Lepe, E. Otárola, and D. Quero
    A posteriori error estimates in $W^{1,p} \times L^p$ spaces for the Stokes system with Dirac measures.
    Computers & Mathematics with Applications, Vol. 94, (2), pp. 47--59, (2021).

19. F. Lepe and G. Rivera
    A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator.
    Calcolo, Vol. 58, (2), pp. 30, (2021).

20. F. Lepe and G. Rivera
    A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem.
    Computer Methods in Applied Mechanics and Engineering, Vol. 379, pp. 113753, (2021).

21. F. Lepe and D. Mora
    Symmetric and nonsymmetric discontinuous Galerkin methods for a pseudostress formulation of the Stokes spectral problem.
    SIAM Journal on Scientific Computing, Vol. 42, 2, pp. A698--A722, (2020).

22. F. Lepe, S. Meddahi, D. Mora, and R. Rodríguez
    Mixed discontinuous Galerkin approximation of the elasticity eigenproblem.
    Numerische Mathematik, Vol. 142, 3, pp. 749--786, (2019).

23. F. Lepe, S. Meddahi, D. Mora, and R. Rodríguez
    Acoustic vibration problem for dissipative fluids.
    Mathematics of Computation, Vol. 88, pp. 45--71, (2019).

24. F. Lepe, D. Mora, and R. Rodríguez
    Finite element analysis of a bending moment formulation for the vibration problem of a non-homogeneous Timoshenko beam.
    Journal of Scientific Computing, Vol. 66, pp. 825--848, (2016).

25. F. Lepe, D. Mora, and R. Rodríguez
    Locking-free finite element method for a bending moment formulation of Timoshenko beams.
    Computers & Mathematics with Applications, Vol. 68, 3, pp. 118--131, (2014).